Q2. A uniform electric field of magnitude N/C points in the positive x-direction. Find the change in electric potential energy of a C charge as it moves from the origin to the points: (a) (0, 6.0 m), (b) (6.0 m, 0), and (c) (6.0 m, 6.0 m).

Background

Topic: Electric Potential Energy in Uniform Electric Fields

This question tests your understanding of how the electric potential energy of a charge changes as it moves in a uniform electric field. It requires you to apply the relationship between electric field, displacement, and potential energy.

Key Terms and Formulas

• Uniform Electric Field (): A field with constant magnitude and direction.

• Electric Potential Difference (): , where is the displacement vector.

• Change in Electric Potential Energy ():

• Charge (): C C

Step-by-Step Guidance

1. Write down the known values: N/C (in the direction), C, and the initial position is the origin .

2. For each part, determine the displacement vector from the origin to the given point. For example, for (a) , m.

3. Calculate the dot product for each case. Remember, points in the direction, so only the -component of contributes to the dot product.

4. Use to find the potential difference for each displacement.

5. Set up the expression for the change in electric potential energy: for each part, but do not compute the final value yet.

Try solving on your own before revealing the answer!