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Q.

The corners A, B, C and D of a square are occupied by charges  q,−q,  2Q  and  Q, respectively. The side of square is 2b.  The field at the midpoint of side CD is zero. What is the value of  q/Q?

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a

55/2

b

22/5

c

2/5

d

5/2

answer is A.

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Detailed Solution

Since the field at midpoint of CD is zero. Hence, EB  cosθ+ED+EA  cosθ−EC=0(q4πε0(5 b)2+q4πε0(5 b)2)cosθ+Q4πε0b2=2Q4πε0b2On solving, we get2q5cosθ=Q  or  2q5(b5 b)=Qor 2q55=Q  or  qQ=552
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