Question:

Consider a uniform electric field E = 500 N/C directed horizontally to the right.

A positive point charge with a magnitude of 4.0 μC is placed at point A as shown below.

a) What is the electric potential difference between points A and B?

b) If the point charge is moved from point C to point D, what is the change in electric potential energy?

c) Is the electric field doing positive or negative work on the charged particle as it moves from point C to point D? Explain your answer.

Answer:

a) The electric potential difference between two points A and B can be calculated using the formula:

ΔV = - Ed

where ΔV is the potential difference, E is the magnitude of the electric field, and d is the displacement between the two points.

In this case, the electric field is directed horizontally, and the displacement d is also horizontal. Therefore, the electric field and the displacement are parallel to each other.

Therefore, the formula becomes:

ΔV = E * d

Given that the electric field E = 500 N/C and the displacement d = 0.5 m (as shown in the figure), we can substitute these values into the formula:

ΔV = 500 N/C * 0.5 m

ΔV = 250 V

Therefore, the electric potential difference between points A and B is 250 V.

b) The change in electric potential energy can be calculated using the formula:

ΔPE = q * ΔV

where ΔPE is the change in electric potential energy, q is the charge, and ΔV is the potential difference.

In this case, the charge q = 4.0 μC = 4.0 × 10^(-6) C, and the potential difference ΔV = 250 V (as calculated in part a).

Substituting these values into the formula, we get:

ΔPE = (4.0 × 10^(-6) C) * (250 V)

ΔPE = 1.0 × 10^(-3) J

Therefore, the change in electric potential energy is 1.0 × 10^(-3) J.

c) The electric field does negative work on the charged particle as it moves from point C to point D.

The reason is that the electric field and the displacement are in opposite directions. The electric field is directed horizontally to the right, while the displacement is in the opposite direction, horizontally to the left.

Since the direction of the force and the displacement are opposite, the work done by the electric field is negative.

Therefore, the electric field does negative work on the charged particle as it moves from point C to point D.