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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 ?
  1. 24cm from+9q
  2. 12cm from+9q
  3. 24cm from+q
  4. 12cm from+q

A
24cm from+9q
B
12cm from+9q
C
24cm from+q
D
12cm from+q
Solution
Verified by Toppr


Two point charges +9q and +9.
Kept apart =16cm=16×102m
Two 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 (16x)cm for the system to remain in equilibrium F1=F2
Therefore,
F1=K(q×Q)x2
F2=K(9q×Q)(16x)2
Equating F1 and F2 we get,
9x2=1(16x)2
F1=F2
or, K(q×Q)x2=K(9q×Q)(16x)2
or, 1x2=9(16x)2
or, 1x=9(16x)
or, 16x=3x
or, 4x=16
or, x=4
(164)cm=12cm from +9q.

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