If `20 J` of work has to be done to move an electric charge of `4 C` from a point, where potential is `10 V` to another point, where potential is V volt, find the value of V.

Options

A. 20 V
B. 30 V
C. 5 V
D. 15 V

Answer

To solve the problem, we need to find the value of the electric potential \( V \) at the second point when a charge of \( 4 \, C \) is moved from a point with a potential of \( 10 \, V \) and \( 20 \, J \) of work is done.

### Step-by-Step Solution:

1. **Identify the known values**:
- Work done \( W = 20 \, J \)
- Charge \( Q = 4 \, C \)
- Initial potential \( V_1 = 10 \, V \)
- Final potential \( V_2 = V \) (unknown)

2. **Use the formula for work done in moving a charge**:
The work done \( W \) in moving a charge \( Q \) through a potential difference \( \Delta V \) is given by:
\[ W = Q \cdot \Delta V \]
where \( \Delta V = V_2 - V_1 \).

3. **Substituting the known values into the equation**:
\[ 20 \, J = 4 \, C \cdot (V - 10 \, V) \]

4. **Rearranging the equation to solve for \( V \)**:
First, simplify the equation:
\[ 20 = 4(V - 10) \]
Divide both sides by \( 4 \):
\[ 5 = V - 10 \]

5. **Solving for \( V \)**:
Add \( 10 \) to both sides:
\[ V = 5 + 10 = 15 \, V \]

### Final Answer:
The value of \( V \) is \( 15 \, V \).