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 V. What is the potential energy of a charge of 5 μC placed at that point?

• A. 0.5 mJ
• B. 1.0 mJ
• C. 2.0 mJ
• D. 5.0 mJ

Hint:

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

Answer 1

The Correct Option is B

Given: Electric field, \( E = 2 \times 10^3 \, \text{N/C} \) 
Potential, \( V = 100 \, \text{V} \) 
Charge, \( q = 5 \, \mu\text{C} = 5 \times 10^{-6} \, \text{C} \) 

Step 1: Formula for Potential Energy The potential energy \( U \) of a charge in an electric field is given by the formula: \[ U = qV \] where: - \( q \) is the charge, - \( V \) is the potential. 

Step 2: Substitute the given values Substitute the given values into the formula: \[ U = (5 \times 10^{-6} \, \text{C})(100 \, \text{V}) \] \[ U = 5 \times 10^{-4} \, \text{J} = 0.5 \, \text{mJ} \] 

Step 3: Conclusion Thus, the potential energy of the charge is \( 0.5 \, \text{mJ} \). 

Answer: The correct answer is option (a): \( 0.5 \, \text{mJ} \).