# Electrical potential difference between planets

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In dealing with electricity, we usually refer to Earth as the electrical neutral or ground. Is there any evidence that other planets' ground is at the same electrical potential level as the Earth's?

If somehow, there was a lossless conductive connection between two planets, would current flow accros It? Would this be theoretically a source of energy?

I dunno how or why a planet would have a significant net charge, but supposing it did, here's some initial calculations.

If the planets have a different net charge, you can treat them as capacitor plates.
Capacitance in its simplest form is

$$C = frac{epsilon *A}{d}$$
The permittivity $$epsilon$$ of vacuum space is 8.85 x 10-12 farad per meter . Let's choose a nearby (nonexistent) planet at 5 LY = 5 * 9.461e+15 m .

Looks like the capacitance is pretty close to zero. So the energy available,

$$E = frac{CV^2}{2}$$ is going to be nonexistent unless there's a seriously large voltage.

## Difference Between Electric Field and Gravitational Field

In physics, electric and gravitational fields are very important concepts. An electric field is a model which is used to explain influences and behaviors of charges and varying magnetic fields. Electric fields are produced by stationary charge particles and varying magnetic fields. So, neutral particles cannot create electric fields. A gravitational field, on the other hand, is a model which is used to explain gravitational phenomena of masses. Even though neutral particles such as neutrons do not interact via electromagnetic forces, they do via gravitational forces. This is the main difference between electric field and gravitational field. This article tries to describe the difference between electric field and gravitational field in detail.

Potential is the specific potential energy. That is, when potential energy depends on some quantity associated with object in question, potential is potential energy per unit of that quantity.

For example, gravitational potential is gravitational potential energy per unit of mass. Electrostatic potential is the electrostatic potential energy per unit of charge.

Potential is simply per unit while Potential energy is per quantity is that all what I am supposed to assume, nothing more complex?

Could you please talk about potential difference specially in connection with Circuits and Point charges.

When you talk about circuits, you are always talking about electrostatic potential. Difference between electrostatic potentials between two points is the voltage. Voltage is the amount of potential energy change for 1 coulomb of charge moving from first point to the second.

If you have a vacuum tube, effectively giving you no resistance, an electron traveling across 1V gap would gain kinetic energy equal to potential energy drop, which is the charge of electron * 1V, or in units of electron charge, this is energy of 1 electron-volt (eV).

In a circuit, however, all this energy is dissipated as heat. If one coulomb of charge moves across 1V of potential, 1J of heat has been produced. Since current is charge flow per unit time, current time voltage gives you amount of energy going into heat per unit of time, or power.

When you say voltage is the amount of potential energy change moving from first point to the second, should I assume that I could find voltage simply by subtracting the potential energy the charge has at the second point from the potential energy the charge had at the first point?

You said 1V gap, I am assuming that the potential at point A would be 5 and point B would be 4 not on the electron but within the field, when you place an electron in the field it will gain potential energy and move due to the potential energy which is now converted into kinetic energy. Am I right? Or potential energy is converted while in progress. All forms of energy are measured in joules so when you say kinetic energy = 34 joules the energy would be the same as saying potential energy = 34 joules. the quantity of energy is the same. So when an electron gains 34 joules of potential energy it will be converted to 34 joules of kinetic energy without any loss except, potential energy would go down to 0 because of the kinetic energy gain.

I am trying to understand this. When an electron is placed in field at point A which has potential 6V the electron will gain potential energy and move. The potential at point B has a potential of 2V, the electron is moving towards B from A. won't there be an affect on the electron as it moves through the different potentials, so when it reaches 4V there might be an affect. What will that be. I am anticipating that when the potential at A is 6V and the potential at B is 6V then the electron will not move. Is that right? Will it gain potential energy? What will be the outcome there? Is it conventional that when an electron has to move between two points the potential at those points has to be the different?

## Planetary science

RSAA partners with the Research School of Earth Sciences (RSES) at ANU to form the the ANU Planetary Science Institute. This collaboration aims to capitalise on the strengths of the two schools to increase our cross-disciplinary understanding of the life cycle and diversity of planets, through discovery and the critical study of the formation, evolution, and fate of planetary systems throughout the Milky Way, including our own Solar System.

Planetary scientists at RSAA study:

• the conditions required for life to form, and where these might occur in our solar system
• the cosmological prerequisites for the formation of terrestrial planets and life
• how to predict and understand the distribution of planets around other stars
• the construction of theoretical models of how planets form from the dusty debris around young stars.

### Searching for extrasolar planets

Astronomers at RSAA are involved in a number of projects that aim to find and study planets outside our own Solar System, and to help answer the universal question of whether life exists elsewhere in the universe.

RSAA is a member of the HAT-South project (Hungarian-made Automated Telescopes), operating two HAT-South telescopes at Siding Spring Observatory. This project is using fully automated arrays of small telescopes at three different locations around the southern hemisphere to monitor hundred of thousands of stars in the galaxy, looking for the characteristic dip in brightness that might signal that an orbiting planet is passing in front of the host star.

Researchers at RSAA, and their colleagues in the project from Princeton University and the Max Planck Institute for Astronomy, analyse the data that is collected for candidate planetary systems, and then perform detailed follow-up observations with larger telescopes to confirm discoveries and measure the density, temperature, and even atmospheric composition of the planets that are found.

## How to determine if a metallic part is an extraneous-conductive-part

It should be verified if parts are deemed to be extraneous-conductive-parts before there may be a requirement to connect them to the MET. The best way to determine whether a conductive part is likely to introduce Earth potential is visual inspection. If it is not possible to determine by visual inspection alone, then a measurement of resistance to Earth can be obtained to determine if the conductive part in question is to be considered an extraneous-conductive-part. Where the measured resistance value between the conductive part concerned and the MET of the installation exceeds the requirements calculated by the equation below, Figure 6.1 taken from IET Guidance Note 8 Earthing and Bonding, the conductive part concerned need not be considered an extraneous-conductive-part as defined in BS 7671:2018. However, the designer must consider the stability of the resistance of the conductive part throughout the lifetime of the installation.

Once the test has been carried out and a value has been obtained, a calculation can be performed to determine if the resistance is low enough for the conductive part to be considered as an extraneous-conductive-part with respect to the safe level of current flow deemed acceptable to the designer.

The values of IB and ZT are taken from BS IEC 60479-1:2018 Effects of current on human beings and livestock. The type of current is 50/60 Hz alternating current.

Firstly, the designer must select a suitable value of ZT which will be different from person to person and is dependent on several factors including (but not limited to)

• The touch voltage
• The supply frequency
• The duration of the current flow
• The conditions of wetness of the skin and surface area in contact
• The general environment.

Table 2 of BS IEC 60479-1:2018, indicates values of total body resistance for hand to hand in wet conditions.

For the purposes of this example, the value of ZT selected is 1000 Ω.

Secondly, the designer must select the acceptable value of IB

• 0.5 mA – The threshold of perception
• 10 mA –- The threshold of let-go or
• 30 mA – a current which can cause effects such as the following, depending on the time which automatic disconnection occurs. Where automatic disconnection occurs within 300 ms (for example, by non-delay RCD with IΔn not exceeding 30 mA): Perception and involuntary muscular contractions, but usually no harmful electrical physiological effects. Longer disconnection time, up to 5 seconds: Involuntary muscular contractions, difficulty in breathing, reversible disturbances of heart function and immobilization, but usually no organic damage.

Looking at the examples below with various values of IB taken from IET Guidance Note 8, if the designer was to select 0.5 mA as a safe level of current through the human body and the measured resistance between the conductive part and the MET is above 459 kΩ, then it need not be considered an extraneous-conductive part, therefore would not require connecting to the main earthing terminal.

## Sunday, November 24, 2013

### Electric Comets: Failures of the Electric Comet Model

With the recent hubub over comets, provided by some Sun-grazers in the news (ISON, Pan-STARS, etc. NASA Comet ISON Observing Campaign) I realized that I did not really have any well-established write-up on the claims about comets made by Electric Universe (EU) supporters. I discovered that I had actually addressed some of these claims a number of times, but always as a part of other claims. So I thought I'd take a quick break from my winter hiatus to assemble some of these into a single post.

Recently, a reader pointed me to some claims being made by the ThunderBolts project in some of their YouTube videos. Most of them are recycled old stuff that keeps getting repeated on a variety of forums.

Periodically, the Electric Universe supporters repeat their claims that comets, like the stars, glow predominantly due to a cathode discharge-type interaction with the Sun. They seem to tie this claim back to some work by Kristian Birkeland but the notion predates Birkeland, and was explored by mainstream astronomers in the late 1800s and early 1900s when electromagnetism was placed on a unified mathematical foundation by Maxwell's Equations and was still the new and exciting force in physics.

EU Claim: The evidence suggests that comets are highly negatively charged with respect to the Sun. As they rush toward the Sun, the voltage increases until at some point the comet nucleus begins to discharge. Electrons are stripped from a few points on the comet surface where the electric field is strongest. These “spark discharges” finely machine rocky material from the surface to form a “cathode jet” of negatively charged dust together with surface matter that has been torn apart to release ionized atoms and molecules, including oxygen.
Prediction #3: Electric Comets and the "Domino Effect"

Laboratory cathodes and anodes form part of a complete circuit. Where is the return circuit between the Sun and the comet? If we see the comet, why don't we see the return path of the particles? In the lab, the return circuit corresponds to the wires connecting the discharge tube to the power source. And just where is the battery or generator that keeps the system energized? To maintain the potential between the Sun and the comet, the return circuit would have to be isolated or insulated as it is in a laboratory environments. Otherwise the comet would quickly 'discharge' and stop glowing.

But even without a solar-system scale voltage, charged particle interactions can take place at the boundary of the comet material moving out and the solar wind moving in. Orbiting spacecraft experience a range of interactions, from ultraviolet solar photons liberating charges from the satellite metal components (photoelectric effect) to charge redistribution on the spacecraft as an otherwise neutral plasma flows around the satellite and the electrons can diffuse more quickly into the wake behind the satellite, generating a small charge separation.

This boundary interaction, similar to the Earth's magnetosphere and the heliospheric termination shock, is common when two different flows meet. Even electrically neutral flows such as the wake of ships moving through water, or aircraft moving through the air, can form these boundary layers where more complex interactions can take place.

EU Claim: While moving between the orbits of Saturn and Uranus (14 times farther from the Sun than the Earth), Comet Halley experienced an outburst between the orbits of Saturn and Uranus that caused dust to stretch over some 300,000 km. At that distance from the Sun, the surface should be in deep freeze at � degrees C.
Prediction #3: Electric Comets and the "Domino Effect"

Again, EU 'theorists' demonstrate incredible misunderstandings in thermodynamics and chemistry. Strange oversight for a group that claims to be 'interdisciplinary'.

This is hardly a problem for the standard comet model where comets have large amounts of carbon dioxide.

Melting and boiling points are different in the low pressure of space.

Most people are familiar with the fact that water boils at lower temperature at higher altitudes. The lower the the pressure exterior to a surface, the easier it is for atoms to 'boil off' of the surface, creating a vapor around the object. Many sensitive instruments launched into space must be allowed to 'outgas' for a time as volatiles trapped in metals and plastics under atmospheric pressure where the satellite was built will begin to escape from surfaces exposed to vacuum. The lower the pressure, the lower the boiling point, for CO2.

While at atmospheric pressure, CO2 sublimates at -78.2C. Drop the pressure and the sublimation point drops even further. At about 1/760 atmospheric pressure, the sublimation point drops to -134.3C (Wikipedia: Carbon dioxide data page). For those unfamiliar with chemistry, the boiling or sublimation point is defined as the temperature where the vapor pressure is equal to the ambient pressure.

In addition, the temperature at the surface of the comet is going to be WARMER than the cloud-tops of planets at the same distance due to the reflectivity of the comet nucleus.

Planets, whose atmospheres are more reflective (30% or higher), will have a lower cloud-top temperature than a comet nucleus at the same distance which has a much lower reflectivity (about 3%), and therefore absorbs more of the radiant heat it receives. The temperature of the surface of a comet in sunlight will be higher than the cloud-tops of a more reflective planet at same distance. Got a layer of snow on your asphalt driveway? Watch how fast it melts around the regions of exposed asphalt when the sun comes out compared to areas completely covered with snow.

EU Claim: "Their surfaces display sharp relief, not what one would expect from melting ice, " On Gravity-centric Cosmology and the Implications of a Universe Awash with Plasma
Section 2.11: Comets as dirty snowballs
by David B. Smith

Even years after the earlier claim noted above, EU theorists don't understand chemistry or thermodynamics. Has Mr. Smith never observed melting snow and shapes that form due to non-uniform heating, melting and refreezing? Perhaps Mr. Smith has only observed ice melting in his glass of tea?

I shoveled plenty of dirty snow for Snowmageddon & Snowpocalypse (wikipedia) and observed the many odd shapes formed as it melted and refroze with the day-night cycle. It's funny that EU 'theorists' could convince others that this was a valid argument when there is so much real world experience with why they are wrong. To paraphrase Sherlock Holmes to Watson: You have SEEN snow, but you have not OBSERVED snow. (Wikipedia: A Scandal in Bohemia)

The ambiguity between comets & asteroids has been known before Thornhill & Talbott
• Evolution of Comets Into Asteroids? (1971)
• Do comets evolve into asteroids - Evidence from physical studies (1982)
Some of these papers point out even earlier sources.

EU Claim: A direct confirmation of the electric connection came unwittingly from the Chandra X-ray Observatory on July 14, 2000. At that time, the Chandra telescope viewed the comet Linear repeatedly over a 2-hour period, detecting unexpected X-rays from oxygen and nitrogen ions in the coma of the comet. The capture of electrons from the negatively charged comet by positively charged hydrogen ions in the solar wind is, of course, nothing else than an electric discharge, nature’s highly efficient means of X-ray production. Prediction #3: Electric Comets and the "Domino Effect"

All of these recombination process happen due to relative motions of atoms, electrons and ions, regardless of how the particles are accelerated. They are in no way evidences for any solar-system scale giant voltage drops of a million volts or more across planetary distances.

Electric Universe supporters now rely on a very ambiguous use of term 'discharge'. EU basically wants to call anything that involves the motion of charges as a 'discharge', a definition so broad as to be technically useless. If moving charges is all that is required, chemical reactions, which alter electron orbital configurations, could also be called a 'discharge' process.

• Charge exchange (Wikipedia)
• Absorption
• stimulated emission (Wikipedia)
• spontaneous emission (Wikipedia)
• photoionization
• 2-body recombination
• dielectronic recombination
• dielectronic absorption (Wikipedia: autoionization) & Compton scattering
• free-free emission (Wikipedia: bremsstrahlung)
• free-free absorption
• collisional excitation (Wikipedia)
• collisional de-excitation
• collisional ionization
• 3-body recombination

EU Claim: "that there would be a double 'flash' consisting of a powerful electric discharge event prior to a very large impact event which would be more explosive than expected, and that radio communication would be interrupted."
On Gravity-centric Cosmology and the Implications of a Universe Awash with Plasma
Section 2.11: Comets as dirty snowballs
by David B. Smith

I've yet to find the original reference of the double flash before the impact AND a radio interruption with this impact event. The only place I can find this is on Electric Universe sites.

Let's see, the spacecraft cameras saw the comet nucleus clearly. The comet nucleus reflects only about 3-4% of the light falling on it, about as dark as a lump of charcoal, and it is being observed against a dark sky slightly brighter due to reflection from the cometary dust material. So it's pretty clear that the camera was adjusted for low-light conditions, much like night-vision goggles. Under those conditions, highly reflective material ejected from the impact point will be really bright, probably more than enough to saturate the camera. Of course it was bright.

Any electrical arc sufficient to light up the region between the comet and spacecraft would have been more than enough to fry the spacecraft electronics, probably with no chance of recovery.

But we have measured electric fields in the solar wind and in the vicinity of comets. Solar wind models combined with spacecraft models enable satellite designers to estimate spacecraft charging as they move through plasmas. Because discharges can kill the satellite electronics, knowledge of these conditions is vital to success of the missions.

Consider these values from the Giacobini-Zinner encounter, which measured +1 volts near the comet vs. +6 volts in the solar wind. This was LOWER than the expected +10 volts (Dynamic PIC-simulations of charging phenomena related to the ice-spacecraft in both cometary and solar wind environments). Considering these are voltages on the scale of batteries you can buy at the corner market, how could this be a "powerful electric discharge"?

After the impact of the probe with the comet nucleus, only a relatively weak x-ray enhancement was detected, so this also makes claims the impact produced an electric discharge as suspect. The additional X-ray emissions were delayed and consistent with charge exchange between the solar wind and outgassed simple molecules.
• Chandra observations of Comet 9P/Tempel 1 during the Deep Impact campaign
• Chandra observations of Comet 9P/Tempel 1 during the Deep Impact campaign
• Swift X-Ray Telescope Observations of the Deep Impact Collision

1. First determination that a comet's surface layer (few to 10 meters or so) is very porous (greater than 75 percent empty space)
2. First direct evidence showing chemical diversity of outgassing associated with different parts of the cometary nucleus
3. Discovered that hyperactive comets (5-10 percent of all comets) are driven by carbon dioxide and that the observed excess water is from icy grains in the coma. The processes of hyperactive comets are very different from those in normal comets.

So lots of CO2 and water found in comets, still in line with the standard model of these objects.

EU Claim: "A forbidden oxygen line was discovered in Comet Austin’s coma. “Forbidden lines” are spectral signatures that are not expected in space because here on Earth they are found only within strong electric fields." -- Wal Thornhill.
Comet Wild 2, January 6, 2004.

Where did Thornhill get bizarre mis-understanding about forbidden lines?

Forbidden lines are created by metastable states in the atom, which have a lifetime much longer than the regular atomic states. Under normal circumstances, these states get de-excited by collisions with other atoms before they have a chance to radiate a photon. However, under extremely low pressures, the states will not be de-excited by collisions and will de-excite by emitting a photon at a frequency correspond to the 'forbidden line'. Electric fields may be in the environment, but they are not required to form forbidden lines.

I suspect Thornhill may be confusing forbidden lines (Wikipedia) with the Stark Effect (Wikipedia) which also has a long history in astronomy.

In spite of repeated claims by Electric Universe supporters to the contrary, the "Dirty Snowball" comet model has been refined, with better details on the composition and structure, but it is far from dead.

Meanwhile Electric Universe supporters continue to echo their support for their model that has a radically different particle and field arrangement for this part of the solar system, while they have yet to provide any model that allows us to to make useful estimates of these quantities. This modeling capability is vital for the safety of satellites and astronauts (see Challenges for Electric Universe 'Theorists').

Yet the standard model, which lacks the million-or more voltages claimed by the Electric Sun advocates, seems to do quite well for protecting our satellites and we continue to explore around the solar system using it (see ADS: An advanced physical model of cometary activity).

So Electric Universe claims continue to be completely useless for doing real spaceflight.

## Dangers of static charge buildup

In addition to causing in a painful shock, these sudden high-voltage discharges can provide a source of ignition for flammable substances, according to the Occupational Safety and Health Administration (OSHA). Static shock can also damage delicate electronics. According to NASA, a simple spark from a finger can damage sensitive components and render them unusable, so precautions must be taken such as keeping circuit boards in conductive plastic bags and wearing grounding straps to dissipate static charge continuously from your body.

Another source of static charge is the motion of fluids through a pipe or hose. If that fluid is flammable &mdash such as gasoline &mdash a spark from a sudden discharge could result in a fire or explosion. People who handle liquid fuels should take great care to avoid charge buildup and sudden discharge. In an interview, Daniel Marsh, professor of physics at Missouri Southern State University, warned that when putting gasoline in your car, you should always touch a metal part of the car after getting out to dissipate any charge that might have developed by sliding across the seat. Also, when buying gas for your lawn mower, you should always take the can out of your car and place it on the ground while filling it. This dissipates the static charge continuously and keeps it from building up enough to create a spark.

Large tank farms present an even greater danger of fire and explosions, so the National Transportation and Safety Board (NTSB) has issued guidelines that include minimizing static generation, preventing charge accumulation, avoiding spark discharge, and controlling the environment inside the tank.

Moving gas and vapor can also generate static charge. The most familiar case of this is lightning. According to Martin A. Uman, author of “All About Lightning” (Dover, 1987), Benjamin Franklin proved that lightning was a form of static electricity when he and his son flew a kite during a thunderstorm. They attached a key to the kite string, and the wet string conducted charge from the cloud to the key which gave off sparks when he touched it. (Contrary to some versions of the legend, the kite was not struck by lightning. If it had been, the results could have been disastrous.)

Franklin in fact shaped the way we think about electricity. He became interested in studying electricity in 1742. Until then, most people thought that electrical effects were the result of mixing of two different electrical fluids. However, Franklin became convinced that there was only one single electric fluid and that objects could have an excess or deficiency of this fluid. He invented the terms "positive" and "negative," referring to an excess or deficiency, according to the University of Arizona. Today, we know that the "fluid" was actually electrons, but those weren't discovered for about 150 years.

According to the Jet Propulsion Laboratory, clouds develop zones of static charge due to warm water droplets in updrafts exchanging electrons cold ice crystals in downdrafts. According to NASA, the potential between these atmospheric charges and the ground can exceed 300,000 volts, so the consequences of being struck by lightning can be deadly. In a lightning strike, the current tends to move over the surface of the body in a process called “external flashover,” which can cause severe burns, particularly at the initial point of contact. Some of the current, though, can travel through the body and damage the nervous system, according to the National Weather Service. Additionally, the concussion from the blast can cause traumatic internal injuries and permanent hearing loss, and the bright flash can cause temporary or permanent vision damage. As an example of the tremendous energy released in a lightning strike, Marsh told Live Science about his personal observation of a large oak tree that was literally split in half by high-pressure steam created by a lightning strike.

If you can hear thunder, generally, you are already within striking range, according to the University of Florida. If you are outdoors when a storm approaches, you should immediately seek shelter in a building or vehicle and avoid touching any metal. If you cannot get inside, move away from tall objects such as trees, towers or hilltops, squat down, and if possible, balance on the balls of your feet making as little contact with the ground as possible, according to Brigham Young University.

## Electrical potential difference between planets - Astronomy

In discussing gravitational potential energy in PY105, we usually associated it with a single object. An object near the surface of the Earth has a potential energy because of its gravitational interaction with the Earth potential energy is really not associated with a single object, it comes from an interaction between objects.

Similarly, there is an electric potential energy associated with interacting charges. For each pair of interacting charges, the potential energy is given by:

electric potential energy: PE = k q Q / r

Energy is a scalar, not a vector. To find the total electric potential energy associated with a set of charges, simply add up the energy (which may be positive or negative) associated with each pair of charges.

An object near the surface of the Earth experiences a nearly uniform gravitational field with a magnitude of g its gravitational potential energy is mgh. A charge in a uniform electric field E has an electric potential energy which is given by qEd, where d is the distance moved along (or opposite to) the direction of the field. If the charge moves in the same direction as the force it experiences, it is losing potential energy if it moves opposite to the direction of the force, it is gaining potential energy.

The relationship between work, kinetic energy, and potential energy, which was discussed in PY105, still applies:

### An example

Two positively-charged balls are tied together by a string. One ball has a mass of 30 g and a charge of 1 the other has a mass of 40 g and a charge of 2 . The distance between them is 5 cm. The ball with the smaller charge has a mass of 30 g the other ball has a mass of 40 g. Initially they are at rest, but when the string is cut they move apart. When they are a long way away from each other, how fast are they going?

Let's start by looking at energy. No external forces act on this system of two charges, so the energy must be conserved. To start with all the energy is potential energy this will be converted into kinetic energy.

Energy at the start : KE = 0
PE = k q Q / r = (8.99 x 10 9 ) (1 x 10 -6 ) (2 x 10 -6 ) / 0.05 = 0.3596 J

When the balls are very far apart, the r in the equation for potential energy will be large, making the potential energy negligibly small.

Energy is conserved, so the kinetic energy at the end is equal to the potential energy at the start:

The masses are known, but the two velocities are not. To solve for the velocities, we need another relationship between them. Because no external forces act on the system, momentum will also be conserved. Before the string is cut, the momentum is zero, so the momentum has to be zero all the way along. The momentum of one ball must be equal and opposite to the momentum of the other, so:

Plugging this into the energy equation gives:

### Electric potential

Electric potential is more commonly known as voltage. The potential at a point a distance r from a charge Q is given by:

Potential plays the same role for charge that pressure does for fluids. If there is a pressure difference between two ends of a pipe filled with fluid, the fluid will flow from the high pressure end towards the lower pressure end. Charges respond to differences in potential in a similar way.

Electric potential is a measure of the potential energy per unit charge. If you know the potential at a point, and you then place a charge at that point, the potential energy associated with that charge in that potential is simply the charge multiplied by the potential. Electric potential, like potential energy, is a scalar, not a vector.

connection between potential and potential energy: V = PE / q

Equipotential lines are connected lines of the same potential. These often appear on field line diagrams. Equipotential lines are always perpendicular to field lines, and therefore perpendicular to the force experienced by a charge in the field. If a charge moves along an equipotential line, no work is done if a charge moves between equipotential lines, work is done.

Field lines and equipotential lines for a point charge, and for a constant field between two charged plates, are shown below:

### An example : Ionization energy of the electron in a hydrogen atom

In the Bohr model of a hydrogen atom, the electron, if it is in the ground state, orbits the proton at a distance of r = 5.29 x 10 -11 m. Note that the Bohr model, the idea of electrons as tiny balls orbiting the nucleus, is not a very good model of the atom. A better picture is one in which the electron is spread out around the nucleus in a cloud of varying density however, the Bohr model does give the right answer for the ionization energy, the energy required to remove the electron from the atom.

The total energy is the sum of the electron's kinetic energy and the potential energy coming from the electron-proton interaction.

The kinetic energy is given by KE = 1/2 mv 2 .

This can be found by analyzing the force on the electron. This force is the Coulomb force because the electron travels in a circular orbit, the acceleration will be the centripetal acceleration:

Note that the negative sign coming from the charge on the electron has been incorporated into the direction of the force in the equation above.

This gives m v 2 = k e 2 / r, so the kinetic energy is KE = 1/2 k e 2 / r.

The potential energy, on the other hand, is PE = - k e 2 / r. Note that the potential energy is twice as big as the kinetic energy, but negative. This relationship between the kinetic and potential energies is valid not just for electrons orbiting protons, but also in gravitational situations, such as a satellite orbiting the Earth.

The total energy is:
KE + PE = -1/2 ke 2 / r = - 1/2 (8.99 x 10 9 )(1.60 x 10 -19 ) / 5.29 x 10 -11

This works out to -2.18 x 10 -18 J. This is usually stated in energy units of electron volts (eV). An eV is 1.60 x 10 -19 J, so dividing by this gives an energy of -13.6 eV. To remove the electron from the atom, 13.6 eV must be put in 13.6 eV is thus the ionization energy of a ground-state electron in hydrogen.

## Can someone explain to me the difference between potential and potential energy in details?And,work done in a conservative force field is the difference in potential or potential energy?

Potential basically tells us the ability of an object to do some work .

And Potential energy is the amount of energy it acquires due to that Potential difference.

#### Explanation:

"NOTE" - Mostly we talk of Potential difference rather than Absolute Potential because it is a relative quantity.

Potential Energy is the energy which arises due to the difference in Potential.

Important observation :-

• Each object in the universe tries to attain low POTENTIAL state.
• That's why electric charges (+ve or -ve) move from region of high potential to low potential.
• Objects fall toward earth in the direction of decreasing POTENTIAL
• Electrons tend to be near the nucleus of the atom #ie# in the region of least potential.

# Potential energy is a relative quantity, it depends on where we choose the potential energy to be Zero (Datum).

Due to difference in vertical height , the Gravitational Potential changes and so does the Gravitational potential energy and this Gravitational potential energy is given by the formula :

#PE_g=mgh# where #m# is the mass of the object #g# is the acceleration due to gravity and #h# is the height above the Datum line (which is the floor/ground normally).

The relation between the Force and Potential is :-
#vecF=-vecgradU# where #F# is the Force and #U# is the potential.

In case of a charged parallel plate Capacitor we can see that due to accumulated opposite charges on the plates a Potential difference is generated #ie# it has ability to do some work and the amount of work it can do is known as the Potential Energy stored inside that capacitor.

The answer is getting quite long, so I can't write more examples I hope it helps :)

## Electrical potential difference between planets - Astronomy

In this problem we will learn about the relationships between electric force , electric field , potential energy , and electric potential . To understand these concepts, we will first study a system with which you are already familiar: the uniform gravitational field.

Because we are in a uniform field, the force does not depend on the object's location. Therefore, the variable does not appear in the correct answer.

 upward downward upward or downward depending on its mass downward only if the ratio of to initial velocity is large enough

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 upward downward upward or downward depending on its charge downward only if the ratio of to initial velocity is large enough

The partial derivative means the derivative of with respect to , holding all other variables constant.

Consider again the electric potential corresponding to the field . This potential depends on the z coordinate only, so and .

Find an expression for the electric field in terms of the derivative of .

Part not displayed

Hint not displayed

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A charge in an electric field will experience a force in the direction of decreasing potential energy. Since the electric potential energy of a negative charge is equal to the charge times the electric potential (), the direction of decreasing electric potential energy is the direction of increasing electric potential.