There is an electric field E in x-direction. If the work done on moving a charge of `0.2C` through a distance of 2 m along a line making an angle `60^@` with x-axis is 4 J, then what is the value of E?

Options

A. `sqrt3N//C`
B. `4N//C`
C. `5N//C`
D. `20N//C`

Explanation

To solve the problem step by step, we will use the formula for work done in an electric field:

### Step 1: Write down the formula for work done
The work done \( W \) on a charge \( q \) moving through a distance \( r \) in an electric field \( E \) is given by:
\[ W = q \cdot E \cdot r \cdot \cos(\theta) \]
where \( \theta \) is the angle between the direction of the electric field and the direction of the displacement.

### Step 2: Identify the known values
From the problem, we have:
- Charge \( q = 0.2 \, \text{C} \)
- Distance \( r = 2 \, \text{m} \)
- Angle \( \theta = 60^\circ \)
- Work done \( W = 4 \, \text{J} \)

### Step 3: Substitute the known values into the formula
Substituting the known values into the work done formula:
\[ 4 = 0.2 \cdot E \cdot 2 \cdot \cos(60^\circ) \]

### Step 4: Calculate \( \cos(60^\circ) \)
We know that:
\[ \cos(60^\circ) = \frac{1}{2} \]
So, substituting this value into the equation gives:
\[ 4 = 0.2 \cdot E \cdot 2 \cdot \frac{1}{2} \]

### Step 5: Simplify the equation
Now, simplify the equation:
\[ 4 = 0.2 \cdot E \cdot 1 \]
\[ 4 = 0.2E \]

### Step 6: Solve for \( E \)
To find \( E \), divide both sides by \( 0.2 \):
\[ E = \frac{4}{0.2} \]
Calculating this gives:
\[ E = 20 \, \text{N/C} \]

### Final Answer
The value of the electric field \( E \) is \( 20 \, \text{N/C} \).

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