When a `2 mu C` charge is carried from point A to point B, the amount of work done by the electric field is `50 mu J`. What is the potential difference and which point is at a higher potential ?

Options

A. `25 V,B`
B. `25 V,A`
C. `20 V,B`
D. both are at same potential.

Explanation

To solve the problem, we will use the relationship between work done, charge, and potential difference. The formula we will use is:

\[ W = Q \cdot V \]

where:
- \( W \) is the work done (in joules),
- \( Q \) is the charge (in coulombs),
- \( V \) is the potential difference (in volts).

### Step 1: Write down the given values
- Work done \( W = 50 \, \mu J = 50 \times 10^{-6} \, J \)
- Charge \( Q = 2 \, \mu C = 2 \times 10^{-6} \, C \)

### Step 2: Rearrange the formula to find the potential difference
We can rearrange the formula to solve for \( V \):

\[ V = \frac{W}{Q} \]

### Step 3: Substitute the values into the formula
Now we substitute the values of \( W \) and \( Q \):

\[ V = \frac{50 \times 10^{-6} \, J}{2 \times 10^{-6} \, C} \]

### Step 4: Perform the calculation
Calculating the above expression:

\[ V = \frac{50}{2} = 25 \, V \]

### Step 5: Determine which point is at a higher potential
Since the work done by the electric field is positive, it indicates that the electric field is doing work on the charge as it moves from point A to point B. This means that point B is at a higher potential than point A.

### Final Answer
The potential difference \( V \) is \( 25 \, V \) and point B is at a higher potential than point A.

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