If 50 joule of work must be done to move an electric charge of 2 C from a point, where potential is -10V to another point where potential is V volt, the value of V is

Options

A. `+ 5 `V
B. `- 15 V `
C. `+ 15 `V
D. `+ 10` V

Answer

To find the value of V, we will use the formula for work done in moving a charge in an electric field. The work done (W) is given by the equation:

\[ W = Q \times (V_f - V_i) \]

where:
- \( W \) is the work done (in joules),
- \( Q \) is the charge (in coulombs),
- \( V_f \) is the final electric potential (in volts),
- \( V_i \) is the initial electric potential (in volts).

Given:
- \( W = 50 \, \text{J} \)
- \( Q = 2 \, \text{C} \)
- \( V_i = -10 \, \text{V} \)
- \( V_f = V \, \text{V} \) (unknown)

Now, substituting the values into the equation:

1. Substitute the known values into the work done formula:
\[ 50 = 2 \times (V - (-10)) \]

2. Simplify the equation:
\[ 50 = 2 \times (V + 10) \]

3. Divide both sides by 2 to isolate the term with V:
\[ 25 = V + 10 \]

4. Subtract 10 from both sides to solve for V:
\[ V = 25 - 10 \]
\[ V = 15 \, \text{V} \]

Thus, the value of \( V \) is \( 15 \, \text{V} \).