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Four point charges Q1, Q2 , Q3 and Q4 are placed at the four corners A, B, C and D of a rectangle having sides 40 cm and 30 cm as shown in figure. Potential at the centre O is found to be 20 volt. If the charge Q4 at corner D is removed, potential at O is found to be 2 volt. Then the value of Q4 is

a
0.5 nc
b
2.5 nc
c
3.75 nc
d
6 nc

detailed solution

Correct option is A

Length  AC=BD=302+402  cm=50  cm.Now,  ∴KQ1AO+KQ2BO+KQ3CO+KQ4DO=Vand  KQ1AO+KQ2BO+KQ3CO=V|Subtracting,  V−V|=KQ4DO⇒20−2=9×109×Q40.25⇒Q4=0.5  nc

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