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Question

Four charges are arranged at the corners of a square ABCD as shown in figure. The force on a positive charge 'Q' kept at the centre of the square is :

A
zero
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B
along diagonal AC
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C
along diagonal BD
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D
perpendicular to the side AB
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Solution

The correct option is D perpendicular to the side ABThe force on +Q at the center of square is,→F=k[−qQ(→r0−→r1)|→r0−→r1|3+qQ(→r0−→r2)|→r0−→r2|3+−2qQ(→r0−→r3)|→r0−→r3|3+2qQ(→r0−→r4)|→r0−→r4|3]=kqQr2[(^i+^j)−(−^i+^j)+2(−^i−^j)−2(^i−^j)]=kqQr2[^i+^j+^i−^j−2^i−2^j−2^i+2^j]=kqQr2(−2^i)thus, F is perpendicular to side AB.

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