SAT Physics Electric Potential - Potential Of Uniform Fields

SAT Physics Electric Potential - Potential Of Uniform Fields

POTENTIAL OF UNIFORM FIELDS
Uniform electric fields are a property of equal and oppositely charged parallel plates. Since the electric field between these plates is uniform, the electric potential is evenly distributed in the space between the plates. Figure 11.1 shows how the electric potential associated with a set of 6-volt plates is commonly visualized.

Figure 11.1. Electric potential for uniform fields

Since the negative plate is low potential, it is often set as the zero point to simplify problems. By definition, the positive plate is considered to be the high potential plate. In this figure, it is set as 6 volts. By definition, the negative plate is the low potential plate. Here it is set as 0 volts. Electric potential is similar to height h in a mechanics problem, where the surface of Earth is the zero point and each meter of height is equally spaced and parallel to Earth.
The magnitude of the electric potential, V, at a location in a uniform electric field can be determined with the following formula.

V=Ed

In this formula distance, d, is measured from a location where the potential is equal to zero to the point in the field where potential is to be solved.
Although charged plates have a uniform electric field between them, the value of the electric potential at each plate is different. In Figure 11.1, the positive plate has a potential of 6 volts and the negative plate has a potential of 0 volts. This difference is known as a potential difference, ΔV. Its value is found by subtracting the two potentials: ΔV =6-0 = 6. The potential difference of charged plates can also be determined with a modified version of the previous equation.

ΔV=EΔd

The electric field, E, of charged plates is uniform and does not change. The distance Ad is the space between the plates.
The electric potential can be viewed as lines that are perpendicular to the electric field and equally spaced. These lines are known as equipotential lines. Every point on a particular equipotential line has the same equal potential. In Figure 11.2, a point P, a positive charge, and a negative charge are all shown at a location where their electric potentials are 4 volts relative to the negative plate. They are all on the same equipotential line.

Figure 11.2. Electric potential

Some problems will ask for the electric potential of a point or charged object located between charged plates. This is calculated with the same equation used to find the potential of the plates themselves, V = Ed. However, the distance, d, is measured from the zero location (usu¬ally the negative plate) to the point or charged object, as shown in Figure 11.2.

Electric Potential of a Uniform Field

Two charged plates with a 20 newton per coulomb electric field are separated by a distance of 10 centimeters. A proton is located at the midpoint between the plates.
(A) Determine the potential difference between the charged plates.
 
WHAT'S THE TRICK?

To find the potential difference of the charged plates, use the formula. Remember to change the distance to meters.

ΔV= EΔd
ΔV = (20 N/C)(0.10 m) = 2 V

(B) Determine the potential acting on the proton.
 
WHAT'S THE TRICK?

You need to find the potential at the point where the proton is located. Since the proton is at the midpoint between the plates, the distance (in meters) is half the distance between the plates.

V= Ed
V = (20 N/C)(0.05 m) = 1 V

POTENTIAL OF POINT CHARGES
The electric potential of point charges is visualized in an entirely different manner and is solved using an entirely different equation than that of uniform fields. The electric field of point charges is radially oriented pointing away from positive charges, and radially oriented toward negative charges. The magnitude of the field has a maximum value at the surface of the charge and becomes weaker with the inverse square of the distance from the center of the charge. It has zero strength at infinity. Although electric potential is not a vector and has no direction, its magnitude follows a similar pattern to that of the electric field surrounding a point charge. Potential has its highest magnitude at the surface of a charge and diminishes to zero at infinity. The lines of equal potential (equipotential lines) are perpendicular to the field and form concentric circles around the charge. An example is shown in Figure 11.3 for a positive charge with a 6-volt potential at its surface.

Figure 11.3. Electric potential of point charges

The equation for potential is very similar to the equation for the electric field. However, potential is a scalar quantity while the electric field is a vector.

Positive charges are considered to have a high positive potential and negative charges have a low negative potential. Although the sign on the charge is important, the distance r from the center of the charge to any point P is set as positive regardless of its direction.

Electric Potential of Several Point Charges
If a problem consists of several point charges surrounding a point P, then merely add together the electric potentials of the individual charges. To find the total potential, simply sum the individual electric potentials.

Electric Potential of Point Charges

A +4 coulomb charge is located 4 meters to the left of the origin. A -4 coulomb charge is located 4 meters to the right of the origin. Determine the electric potential at point P located at the origin.
 
WHAT'S THE TRICK?

The charges are spherical. Use the potential equation for point charges.
Since there are two charges, add them. The sign on the charges is important. However, the sign on the distance from the origin is not.

ELECTRIC POTENTIAL ENERGY
Once the electric potential at a point in space is determined, any charge q can be inserted at that point and the electric potential energy, U_E, can be determined. Simply multiply the electric potential, V, at a point in space by the charge, q, located at that point.

U_E = qV

The relationship between electric potential and electric potential energy is similar to that between electric field and electric force. A point in space will have a specific electric field value, E, and a specific electric potential value, V. When a charge, q, is placed at a point in space, the electric field creates a force, F_E, on the charge. The electric potential can be used to determine its electric potential energy, U_E.

F_E = qE    and    U_E = qV

Whether the electric potential is due to charged plates, a single point charge, or several point charges, the equation to find electric potential energy is the same. In Figure 11.4(a), a point charge q is located in the uniform field of charged plates. In Figure 11.4(b), a point charge q₂ is located in the electric field created by point charge q₁

Figure 11.4. Electric potential energy

You can substitute the equations for electric potential, V, into the equations found in Figure 11.4(a) and Figure 11.4(b) to create alternate equations for electric potential energy.

The resulting equations solve for electric potential energy without the need to determine electric potential. Electric potential energy is very similar to gravitational potential energy. These derived equations bear strong resemblances to the equations for gravitational potential energy.

Potential energy, U, is the energy of position. When objects are released, they lose their potential energy doing work. The lost energy is usually converted into kinetic energy. As a result, electric potential energy, U_B can be thought of as the potential to move charges. Elec­tric potential, V, is directly proportional to electric potential energy. In an electrical circuit or in problems involving the motion of charges, electric potential can be thought of as an electrical pressure that exists at a point in space or in a circuit. Any charge located at that point will have the energy needed to move. Electric potential is also commonly called voltage. High voltage is a high potential for charges to move and thus a greater chance of receiving an electric shock.