Question

A charge of 5 C is moved from a point P to another point Q by doing a work of 10 J. If the potential at P is 0.5 V, then the potential at Q is:

• A. 1.0 V
• B. 2.0 V
• C. 2.5 V
• D. 1.5 V
• E. 3.0 V

Hint:

Potential difference is the work done per unit charge.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This problem relates work done in moving a charge between two points in an electric field to the electric potential difference between those points.
Step 2: Key Formula or Approach:
The work done (W) by an external agent to move a charge (q) from a point P to a point Q is equal to the charge multiplied by the change in electric potential (the potential difference) between the two points. \[ W_{P \to Q} = q \times \Delta V = q \times (V_Q - V_P) \] where \( V_Q \) is the potential at point Q and \( V_P \) is the potential at point P. Step 3: Detailed Explanation:
We are given: - Charge, \( q = 5 \text{ C} \) - Work done, \( W = 10 \text{ J} \) - Potential at P, \( V_P = 0.5 \text{ V} \) We need to find the potential at Q, \( V_Q \). Substitute the given values into the formula: \[ 10 = 5 \times (V_Q - 0.5) \] First, solve for the potential difference \( (V_Q - V_P) \). Divide both sides by 5: \[ \frac{10}{5} = V_Q - 0.5 \] \[ 2 = V_Q - 0.5 \] Now, solve for \( V_Q \) by adding 0.5 to both sides: \[ V_Q = 2 + 0.5 = 2.5 \text{ V} \] Step 4: Final Answer:
The potential at Q is 2.5 V.