Question

A point charge of 2 C experiences a constant force of 1000 N when moved between two points separated by a distance of 2 cm in a uniform electric field. The potential difference between the two points is

• A. 12 V
• B. 8 V
• C. 10 V
• D. 16 V
• E. 5 V

Hint:

Always ensure your units are in SI before calculating. Converting 2 cm to 0.02 m is the most common place to make a mistake in this type of problem!

Answer 1

The Correct Option is C

Concept: This problem relates the force on a charge in an electric field to the work done and the resulting potential difference.
• Electric Field Strength (\(E\)): \(E = F/q\).
• Potential Difference (\(V\)): In a uniform field, \(V = E \cdot d\).
• Alternative: Potential difference is work done per unit charge (\(V = W/q\)).

Step 1: Calculate the Work Done (\(W\)).
Work done is force multiplied by displacement in the direction of the force: Given \(F = 1000 \text{ N}\) and \(d = 2 \text{ cm} = 0.02 \text{ m}\). \[ W = F \cdot d = 1000 \times 0.02 = 20 \text{ Joules} \]

Step 2: Determine the Potential Difference (\(V\)).
Using the definition of potential as work per unit charge: Given \(q = 2 \text{ C}\). \[ V = \frac{W}{q} = \frac{20 \text{ J}}{2 \text{ C}} = 10 \text{ Volts} \]