Electric Potential Quiz

PDF page 586: As you learned in studying gravity, a mass in a gravitational field has potential energy, which means it has the potential to accelerate and thereby increase its kinetic energy. This kinetic energy can be used to do work. For example, imagine you want to use a stone to pound a nail into a piece of wood. You first lift the stone high above the nail, which increases the potential energy of the stone-Earth system—because Earth is so large, it does not move, so we usually shorten this by saying simply that the potential energy of the stone increases. When you drop the stone, gravity converts the potential energy into kinetic energy. When the stone hits the nail, it does work by pounding the nail into the wood. The gravitational potential energy is the work that a mass can potentially do by virtue of its position in a gravitational field. Potential energy is a very useful concept, because it can be used with conservation of energy to calculate the motion of masses in a gravitational field. Electric potential energy works much the same way, but it is based on the electric field instead of the gravitational field. By virtue of its position in an electric field, a charge has an electric potential energy. If the charge is free to move, the force due to the electric field causes it to accelerate, so its potential energy is converted to kinetic energy, just like a mass that falls in a gravitational field. This kinetic energy can be used to do work. The electric potential energy is the work that a charge can do by virtue of its position in an electric field. The analogy between gravitational potential energy and electric potential energy is depicted in Figure 18.21. On the left, the ball- Earth system gains gravitational potential energy when the ball is higher in Earth's gravitational field. On the right, the twocharge system gains electric potential energy when the positive charge is farther from the negative charge.

PDF page 587: energy is of the Earth-ball system. On the right, the electric field points toward a negative charge. The farther the positive charge is from the negative charge, the higher the potential energy is of the two-charge system.

PDF page 586: As you learned in studying gravity, a mass in a gravitational field has potential energy, which means it has the potential to accelerate and thereby increase its kinetic energy. This kinetic energy can be used to do work. For example, imagine you want to use a stone to pound a nail into a piece of wood. You first lift the stone high above the nail, which increases the potential energy of the stone-Earth system—because Earth is so large, it does not move, so we usually shorten this by saying simply that the potential energy of the stone increases. When you drop the stone, gravity converts the potential energy into kinetic energy. When the stone hits the nail, it does work by pounding the nail into the wood. The gravitational potential energy is the work that a mass can potentially do by virtue of its position in a gravitational field. Potential energy is a very useful concept, because it can be used with conservation of energy to calculate the motion of masses in a gravitational field. Electric potential energy works much the same way, but it is based on the electric field instead of the gravitational field. By virtue of its position in an electric field, a charge has an electric potential energy. If the charge is free to move, the force due to the electric field causes it to accelerate, so its potential energy is converted to kinetic energy, just like a mass that falls in a gravitational field. This kinetic energy can be used to do work. The electric potential energy is the work that a charge can do by virtue of its position in an electric field. The analogy between gravitational potential energy and electric potential energy is depicted in Figure 18.21. On the left, the ball- Earth system gains gravitational potential energy when the ball is higher in Earth's gravitational field. On the right, the twocharge system gains electric potential energy when the positive charge is farther from the negative charge.

PDF page 587: energy is of the Earth-ball system. On the right, the electric field points toward a negative charge. The farther the positive charge is from the negative charge, the higher the potential energy is of the two-charge system.

PDF page 587: potential energy is the work done by the electric field to move a charge q from an initial position to a final position (

PDF page 588: If the electric field is not constant, then the equation is not valid, and deriving the electric potential energy becomes more involved. For example, consider the electric potential energy of an assembly of two point charges and of the same sign that are initially very far apart. We start by placing charge at the origin of our coordinate system. This takes no electrical energy, because there is no electric field at the origin (because charge is very far away). We then bring

PDF page 588: charge in from very far away to a distance r from the center of charge . This requires some effort, because the electric field

PDF page 588: of charge applies a repulsive force on charge . The energy it takes to assemble these two charges can be recuperated if we

PDF page 588: be used to do work. The maximum amount of work the two charges can do (if they fly infinitely far from each other) is given by the equation above. Notice that if the two charges have opposite signs, then the potential energy is negative. This means that the charges have more potential to do work when they are far apart than when they are at a distance r apart. This makes sense: Opposite charges attract, so the charges can gain more kinetic energy if they attract each other from far away than if they start at only a short distance apart. Thus, they have more potential to do work when they are far apart. Figure 18.23 summarizes how the electric potential energy depends on charge and separation.

PDF page 589: Normally, the electric potential is simply called the potential or voltage. The units for the potential are J/C, which are given the name volt (V) after the Italian physicist Alessandro Volta (1745–1827). From the equation , the electric potential a distance r from a point charge is

PDF page 589: Normally, the electric potential is simply called the potential or voltage. The units for the potential are J/C, which are given the name volt (V) after the Italian physicist Alessandro Volta (1745–1827). From the equation , the electric potential a distance r from a point charge is

PDF page 590: derived by considering the electric field. Electric fields follow the principle of superposition and can be simply added together, so the electric potential from different charges also add together. Thus, the electric potential of a point near a group of charges is

PDF page 590: that the electric field can be written as Notice from the equation 18.30

PDF page 590: which means that the electric field has units of V/m. Thus, if you know the potential difference between two points, calculating the electric field is very simple—you simply divide the potential difference by the distance!

PDF page 590: which means that the electric field has units of V/m. Thus, if you know the potential difference between two points, calculating the electric field is very simple—you simply divide the potential difference by the distance!