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

Options

A. `3N//C`
B. `4N//C`
C. `5N//C`
D. `20N//C`

Answer

To find the value of the electric field \( E \) given the work done on a charge, we can follow these steps:

### Step 1: Understand the relationship between work, force, and displacement
The work done \( W \) on a charge \( q \) when it moves through a distance \( s \) in an electric field \( E \) can be expressed as:
\[ W = F \cdot s \cdot \cos(\theta) \]
where \( F \) is the force acting on the charge, \( s \) is the distance moved, and \( \theta \) is the angle between the force and the direction of displacement.

### Step 2: Relate force to electric field
The force \( F \) acting on a charge \( q \) in an electric field \( E \) is given by:
\[ F = qE \]
Substituting this into the work equation gives:
\[ W = qE \cdot s \cdot \cos(\theta) \]

### Step 3: Substitute the known values
From the problem, we know:
- Work done \( W = 4 \, \text{J} \)
- Charge \( q = 0.2 \, \text{C} \)
- Distance \( s = 2 \, \text{m} \)
- Angle \( \theta = 60^\circ \)

Now, substituting these values into the equation:
\[ 4 = (0.2)E \cdot (2) \cdot \cos(60^\circ) \]

### Step 4: Calculate \( \cos(60^\circ) \)
The cosine of \( 60^\circ \) is:
\[ \cos(60^\circ) = \frac{1}{2} \]

### Step 5: Substitute \( \cos(60^\circ) \) into the equation
Now we can substitute \( \cos(60^\circ) \) into the equation:
\[ 4 = (0.2)E \cdot (2) \cdot \left(\frac{1}{2}\right) \]

### Step 6: Simplify the equation
This simplifies to:
\[ 4 = (0.2)E \cdot 1 \]
\[ 4 = 0.2E \]

### Step 7: Solve for \( E \)
To find \( E \), divide both sides by \( 0.2 \):
\[ E = \frac{4}{0.2} = 20 \, \text{N/C} \]

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

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