Question

There is an electric field E in the +x-direction. If the work done by the electric field in moving a charge 0.2 C through a distance of 2m along a line making an angle of ${60^0}$ with the x-axis is 1.0 J, what is the value of E in $N{C^{ - 1}}$?

Answer 1

Hint: Here we go through by applying the formula of work done on an electric charge in some given electric field. And by that formula we will be able to find out the value of the electric field.
Formula used: - $W = \overrightarrow F \cdot \overrightarrow r $, $F = qE$

Complete Step-by-Step solution:
Here in the given question it is given that the work done by the electric field in moving a charge 0.2 C through a distance of 2m along a line making an angle of ${60^0}$ with the x-axis is 1.0 J.
It means that,
W=1.0 j=1.0 Nm we have to convert the joule into Newton meter because we have to give the answer and we have to give the answer in terms of Newton.
r=2m
$\theta = {60^0}$
Q=0.2 C
And we have to find the magnitude of the electric field (E).
As we know that $W = \overrightarrow F \cdot \overrightarrow r $
So we can write it as by solving dot product as,
$W = Fr\cos \theta $ And we also know that force (F) =qE so we can say,
$W = qEr\cos \theta $ And we will put the given values in the formula to find out the value of E.
$
   \Rightarrow 1Nm = 0.2C \times E \times 2m \times \cos {60^0} \\
   \Rightarrow E = \dfrac{{1 \times Nm}}{{0.2C \times 2m \times \cos {{60}^0}}} = \dfrac{1}{{0.2 \times 2\left( {\dfrac{1}{2}} \right)}} = 5N{C^{ - 1}} \\
 $
 As we know the value of $\cos {60^0} = \dfrac{1}{2}$.
Hence the required value of E is $5N{C^{ - 1}}$.

Note: - Whenever we face such type of question the key concept for solving the question is to first write the given data of the question and apply the formula on the basis of the given data and find out the unknown terms which we have to find out and always take of given units and in which units we have to give the answers.