There is and electric field E in the +x direction. If the work done by the electric field in moving a charges `0.2C` through a distance of 2m along a line making an angle of `60^(@)` with the x-axis is `1.0J`, what is the value of E in `NC^(-1)`?

Explanation

To solve the problem step by step, we will use the formula for work done in an electric field and the relationship between force, electric field, and charge.

### Step 1: Understand the Work Done Formula
The work done \( W \) by an electric field when moving a charge \( q \) through a distance \( d \) at an angle \( \theta \) with respect to the direction of the electric field \( E \) is given by:
\[ W = F \cdot d \cdot \cos(\theta) \]
where \( F \) is the force acting on the charge.

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

### Step 3: Substitute Known Values
From the problem, we know:
- \( W = 1 \, \text{J} \)
- \( q = 0.2 \, \text{C} \)
- \( d = 2 \, \text{m} \)
- \( \theta = 60^\circ \)

Now, substituting these values into the equation:
\[ 1 = (0.2 \cdot E) \cdot 2 \cdot \cos(60^\circ) \]

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

### Step 5: Simplify the Equation
This simplifies to:
\[ 1 = (0.2 \cdot E) \cdot 1 \]
Thus, we have:
\[ 1 = 0.2 \cdot E \]

### Step 6: Solve for Electric Field \( E \)
To find \( E \), we rearrange the equation:
\[ E = \frac{1}{0.2} \]
Calculating this gives:
\[ E = 5 \, \text{N/C} \]

### Final Answer
The value of the electric field \( E \) is:
\[ E = 5 \, \text{N/C} \]