Question

# Two point charges +9q and +q are kept 16 cm apart. Where should a third charge Q be placed between them so that the system remains in equilibrium ?

A
24cm from+9q
B
12cm from+9q
C
24cm from+q
D
12cm from+q
Solution
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#### Two point charges +9q and +9. Kept apart =16cm=16×10−2mTwo cases will be needed.Given charges, +q, +9q. let, the third charge q be placed at a distance x from q and hence its distance from 9q and (16−x)cm for the system to remain in equilibrium F1=F2Therefore, F1=K(q×Q)x2F2=K(9q×Q)(16−x)2Equating F1 and F2 we get,9x2=1(16−x)2F1=F2or, K(q×Q)x2=K(9q×Q)(16−x)2or, 1x2=9(16−x)2or, 1x=9(16−x)or, 16−x=3xor, 4x=16or, x=4∴ (16−4)cm=12cm from +9q. 4
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