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Question

Equal charges Q are placed at the four corners A,B,C and D of a square of length a. The magnitude of the force on the charge at B will be
  1. 3Q24πε0a2
  2. 4Q24πε0a2
  3. kQ2a2(22+12)
  4. (2+12)3Q24πε0a2

A
(2+12)3Q24πε0a2
B
3Q24πε0a2
C
kQ2a2(22+12)
D
4Q24πε0a2
Solution
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Step 1: Draw the figure and mention the direction of forces at B.[Ref. Fig.]

Step 2: Calculate the force experienced by B due to other charges
Applying Coulomb's law,
Force on B due to charge at A,FA=14π0Q2a2

Force on B due to charge at C,FC=14π0Q2a2

Force on B due to charge at D,FD=14π0Q22a2

Step 3: Net resultant force on B

Resultant of FA and FC,F=F2A+F2C

=14π0Q2a2+14π0Q2a2

=24π0Q2a2

Net force at B=F+FD {Both are in the same direction}

=2Q24π0a2+14π0Q22a2

=(22+12)Q24π0a2 =(22+12)KQ2a2
Hence, Option(C) is correct.

2111120_1504455_ans_67d065f20da4433e94529239ab5a16bc.png

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