Question

The electric field at a point in space is \( 2 \times 10^3 \, \text{N/C} \) and the potential at the same point is \( 100 \, \text{V} \). What is the potential energy of a charge of \( 5 \, \mu\text{C} \) placed at that point?

• A. \( 0.5 \, \text{mJ} \)
• B. \( 1.0 \, \text{mJ} \)
• C. \( 2.0 \, \text{mJ} \)
• D. \( 5.0 \, \text{mJ} \)

Hint:

Remember: The potential energy of a charge in an electric field is the product of the charge and the electric potential at the point where the charge is located.

Answer 1

The Correct Option is B

Step 1: Apply the potential energy formula The potential energy \( U \) for a charge \( q \) in an electric field is calculated using: \[ U = qV \] where: - \( q \) represents the charge, - \( V \) represents the electric potential at the location. Step 2: Input provided values Provided data: - \( q = 5 \, \mu\text{C} = 5 \times 10^{-6} \, \text{C} \) - \( V = 100 \, \text{V} \) Insert these values into the formula: \[ U = 5 \times 10^{-6} \times 100 = 5 \times 10^{-4} \, \text{J} = 1.0 \, \text{mJ} \] Answer: The potential energy of the charge is \( 1.0 \, \text{mJ} \). This corresponds to option (2).