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6. Electric Potential and Capacitance

- When an object moves in a field of gravity, it can experience a change in energy due to the work done on it.
- When a charge moves in an electric field, it generally experiences a change in energy due to the work done on it by the electric field.
- We can simplify our calculations of work and energy changes by exploring the idea of electric potential.

- The electric force works on the charge if its displacement is always parallel to the field.

- The electric force that the charge feels is constant since the field is uniform.

- When the field does positive work, the change in potential energy is negative, which means that potential energy has decreased.
- It's similar to dropping a rock to the ground, because gravity does positive work and the rock loses energy.

- The previous problem should be considered in the case of a negative charge.

- The electric force naturally pushes negative charges against field lines, so an outside agent must be pushing the charge to make it move.
- The work done by the electric field is expected to be negative.
- The electric force points in the opposite direction to the displacement, so the work it does is W E. When the field does negative work, the potential energy increases because the change in potential energy is positive.
- It's similar to lifting a rock off the ground, with gravity doing negative work and the rock gaining potential energy.

- The electric force felt by q is equal to E because q is positive.

- The electric force doesn't work along r 1 because of the displacement.
- The work done by the electric field as q moves from A to B is the same as the work it does along r 2.
- W E is the same as before since the length of r 2 is d.

- A positive charge q 1 is held stationary while a negative charge q 2 is released from rest at a distance of 10 cm from q 1 When it's 1 cm from q 1 you can find the energy of charge q 2.

- The gain in energy is equal to the loss in energy.
- We were able to use the equation for work from a constant force when we looked at constant electric fields.
- We need another equation when the field changes.

- Since q 2 lost potential energy, the gain is 0.016 J.
- This is the energy of q 2 when it's 1 cm from q 1

- Two positive charges, q 1 and q 2, are held in the positions shown below.

- The positive work done by an external agent is equal to the negative work done by the electric force as it is brought into place.
- The electric force is used to compute the work done by q 3.
- The work done on q 3 by the electric force is equal to the work done on q 3 by the electric force.

- Electric Potential and Electric Potential Energy are not the same thing.

- As the electric field on a charge q undergoes a displacement, let W E be the work done by it.
- The electric force on the second charge would be twice as great as on the first charge, and the work done by the electric field would be twice as much.
- Since the work would be twice as much in the second case, the change in electrical potential energy would be twice as great, but the ratio of the change in potential energy to the charge would be the same.
- The work done by the field and the displacement is what this ratio shows.

- There is a similar concept.
- The work done by gravity near the Earth is called D W. The work would have to be D W if the mass were moved twice.
- The ratio of the work to the mass moved is technically the "gravitational potential," but near the Earth, this quantity is simply the gravity of the object.
- A change in height is equivalent to a change in electric potential.

- The units of electric potential are joules per coulomb.
- One joule per coulomb is called one V.

- It's meaningless to find the potential at a single point in space.
- Initial and final positions are more important with potential.
- If there is no relation to another point, finding the potential energy at a certain point is meaningless.
- We can generate energy when we move a charge across it.
- In the next chapter there will be a need for a potential difference in order to have an electrical circuit.

- The electric field is created by a point source charge.

- The potential is dependent on the strength of the source charge and the distance from it.

- The work done by the electric field on a charge of q coulombs brought to a point 2 cm from Q would be 900 q joules.

- Electric potential is similar to potential energy.
- We didn't have to specify the direction of the vector from the position of Q to the Point P because it didn't matter.
- A sphere with a surface of 2 cm from Q will have a potential of 900 V. The equipotentials are always in line with the electric field lines.

- Equipotential surfaces are not real.
- The electric potential in that region doesn't change if we put a metal sphere in that location or if we visualize a sphere that isn't really there.

- The potential, V, never changes if the charge stays on a single equipotential.
- U E is zero.
- The work done by the electric field is zero.

- The formula V is used to find the potential due to a single point source charge.
- We won't be concerned with orientation just the sign of charge.
- We're adding numbers when we add up individual potentials.

- The electric force is conservative.
- The change in position is the most important factor when calculating potential energy.

- Ordinary numbers are added by potentials.
- The potential at A is the sum of the potentials at A due to q 1 and q 2.
- The distance from q 1 to A is 5 cm.

- The data from example 8 is being used.

- If we divide the potential difference between Points A and B by q, we can see the change in the electrical potential energy.

- The work is required to move q from A to B.

- A is a point on the plate and B is a distance from the sheet.

- The potential decreases as we move away from the plate.

- Two large flat plates are separated by a distance.
- There is an electric field between the plates.
- Determine the difference between the plates.

- The amount Ed tells us that the potential of the positive plate is greater than the potential of the negative plate.

- The magnitude of the electric field can be determined quickly if the potential difference and the distance between the plates are known.

- The Capacitor can be seen as a dam in a river in terms of a circuit.
- There is water in the balloon.
- Unless you blow a lot harder, no more air will go into the balloon unless air pressure pushes on one side.

- Two conductors, separated by some distance, carry equal but opposite charges.
- A system called a Capacitor is comprised of a pair of conductors.
- Potential energy is stored if work is done to create a separation of charge.
- Capacitors are used to store potential energy.

- The most common conductors are metal plates or sheets.
- These types ofCapacitors are called parallel-plateCapacitors.
- Since the electric field between the plates is uniform, we assume that the distance between the plates is small.
- If the surface charge density is positive, the electric field will be due to one plate, if it is negative, it will be due to two plates.

- The charge on theCapacitor, Q, or the potential difference, V, across it, is not determined by the Capacitance.
- The relationship between Q and V is shown in the 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 888-666-1846 The amount of charge we can hold on the capacitor depends on the amount of voltage applied to it.
- The area of the plates and the separation between the plates are the two things that determine capacitance.

- The capacity for holding charge is measured by the capacitance.
- The more charge can be stored on the plates at a given potential difference.
- The size, shape, and separation of conductors and the "dielectric constant", k, are only some of the factors that affect the capacitance.
- If there is no gap between the plates, then k is 1.
- The units of C are coulombs.
- One farad (abbreviated F): 1 C/V is the new coulomb.

- A 10-nanofarad parallel-plateCapacitor has a charge of 50 magnitudeuC on each plate.

- In the preceding chapter, we noticed that the electric field created by one or more point source charges varied depending on the location.
- The electric field gets weaker as we move further away from the source charge.
- The direction of the field changes as we move around, even if we stay at the same distance.
- We couldn't get an electric field that was constant in both magnitude and direction from point-source charges.
- The electric field that is created between the plates of a charged parallel-plate capacitor is constant in both magnitude and direction throughout the region between the plates.
- The electric field, E, always points from the positive plate to the negative plate, and its magnitude remains the same at every point between the plates, whether we choose a point close to the positive plate, closer to the negative plate, or between them.

- The equation for calculating E is equally straightforward because it is the same everywhere.

- The units of E are shown in the equation F + qE.
- Ed tells us that the units of E are V/m.
- The units used for the electric field are the same as newtons-per-coulomb and volts-per-meter.

- The plates of a parallel-plate Capacitor are separated by 2mm.
- The device has a capacitance of 1 mF.

- A positive charged plate of a parallel-plateCapacitor is placed on top of a protons mass, as shown below.

- The charge is Q and the capacitance is C. If the electric field in the region between the plates has a magnitude E, give an expression that shows how long it will take for the protons to move up to the other plate.

- The time it will take for the protons to move the distance is determined by using a kinematics equation with v 0 and d. The force that the protons feels is F / m, where qE is the force that the protons feels.
- The expression V becomes eQ/mdC for a. q is for a protons.

- Take a small amount of negative charge off the positive plate and transfer it to the negative plate in order to figure out the electrical potential energy stored in aCapacitor.
- Positive work done by an external agent is the reason that the energy is stored.
- If the final charge is Q, then we transferred an amount of charge equal to Q, fighting against the prevailing voltage at each stage.

- The potential energy is stored in a Capacitor.

- electrons are free to pass if we place a conductor.

- One way to keep the plates of aCapacitor apart is to put an Insulated between them.

- There is always an increase in the capacitance of theCapacitor.

- Attach a dielectric to theCapacitor from the charging source.
- There is more electron density on the side of the molecule near the positive plate because the electric field between the plates causes the molecule to polarize.

- The effect of this is to form a layer of negative charge along the top surface of the dielectric and a layer of positive charge along the bottom surface.

- The electric field has been reduced from its previous value.

- The value of k varies from material to material, but is always greater than 1.

- Chapter 12 contains solutions.

- An experiment is conducted and data is gathered for the electric potential V at various positions away from a uniformly charged sphere.
- Outside of the sphere, all measurements are taken.

- A charge q experiences a displacement in the electric field from position A to position B.

- The length of the line segment is 10 cm and the length of the curved path is 20 cm.

- All four charges are located at the corners of the square.

- There is a parallel-plate Capacitor in the figure below.
- The plates are separated by a distance and each has a length and width.

- An electron is shot horizontally into the empty space between the plates, with an initial velocity of magnitude v 0 The electron misses hitting the end of the top plate.

Write your answer in terms of L, d, m, e, and v 0

- An excess charge of Q is carried by a sphere of radius.

- The voltage is the electric potential.
- The electrical potential energy is determined by the following numbers.
- The work done moving a charge through an electric field is given by W. A Capacitor is a storage device.
- The 888-405-7720 888-405-7720 A is the area of the plate, and d is the distance between the plates.
- When there is a vacuum between the plates of the capacitor, its capacitance increases.
- The electrical energy is given by either UC or QV.

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