`A` and `B` are two points in an electric field . If the work done in carrying `4.0 C` of electric charge from `A` to `B` is `16.0 J`, the potential difference between `A` and `B` is

Options

A. zero
B. `2.0 V`
C. `4.0 V`
D. `16.0 V`

Explanation

To find the potential difference between points A and B in an electric field, we can use the formula that relates work done (W), charge (Q), and potential difference (ΔV):

\[ W = Q \cdot \Delta V \]

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

Given:
- Work done, \( W = 16.0 \, J \)
- Charge, \( Q = 4.0 \, C \)

We need to find the potential difference \( \Delta V \).

### Step 1: Rearranging the formula
We can rearrange the formula to solve for \( \Delta V \):

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

### Step 2: Substituting the values
Now we will substitute the given values into the rearranged formula:

\[ \Delta V = \frac{16.0 \, J}{4.0 \, C} \]

### Step 3: Performing the calculation
Now, we perform the division:

\[ \Delta V = 4.0 \, V \]

### Conclusion
The potential difference between points A and B is \( 4.0 \, V \).

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