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There is a uniform electric field in X-direction. If the work done in a moving charge of 0.2 C through a distance of 2 meter along the line making an angle 60 degree with X-direction is 4 joules, then the value of E is:
(A) \[\sqrt 3 N/C\]
(B) $4N/C$
(C) $5N/C$
(D) $20N/C$

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Last updated date: 17th Apr 2024
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Answer
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Hint: In order to this question we will put all the values in the relation which is between all these quantities and by translating all these we will get the required answer. Specifically for this question we will be putting the formula of work done in which the factors of electric field, separation between charge and electric field and angle is given.

Complete step by step solution:
For solving this question we will have to fetch for the relation between the electric field and the work done but there is not any such relation directly given to us or we have not studied it before.
But as we know the relation between the work done and the force which is work done by the force is the cross product of force and the distance travelled by it. So,
$W = F \times d$
Which can also be written as
$W = Fd\cos \theta $ according to the vector cross product.
And we also know that the force by an electric charge is equal to charge multiplied by electric field so we can write it as:
$W = qEd\cos \theta $
Now transforming all the values other side and putting the electric field on one side so:
$E = \dfrac{W}{{qd\cos \theta }}$
Now we have reached at the end point of our question so by putting all the values in this question we will get:
$E = \dfrac{4}{{2 \times (0.2) \times \dfrac{1}{2}}}$
So by calculating this we will get
$E = 20N/C$

So our correct option is D.

Note:
It can be typical and even more difficult to learn the direct formula $W = qEd\cos \theta $ so it is more appropriate to take with basic and not to go for every single thing which can be remind from the start, it will make the concept more clear every single time we will use it and the concept of work will also be reminded is the another benefit of it.