two charges q and -3q are fixed on x-axis separated by distance d. where should a third charge 2q be placed from A such that it will not experience any force?
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Suppose the third charge is placed at P.
For the force experienced by the third at P to be zero, the net electric field at P must be zero.
From the diagram, the net field at P is,
E = k(8 × 10-6)/(0.2 + x)2 + k(-2 × 10-6)/x2
=> 0 = k(8 × 10-6)/(0.2 + x)2 + k(-2 × 10-6)/x2
=> 0 = 4/(0.2 + x)2 - 1/x2
=> 1/x2 = 4/(0.2 + x)2
=> 1/x = 2/(0.2 + x)
=> 0.2 + x = 2x
=> x = 0.2 m
For the force experienced by the third at P to be zero, the net electric field at P must be zero.
From the diagram, the net field at P is,
E = k(8 × 10-6)/(0.2 + x)2 + k(-2 × 10-6)/x2
=> 0 = k(8 × 10-6)/(0.2 + x)2 + k(-2 × 10-6)/x2
=> 0 = 4/(0.2 + x)2 - 1/x2
=> 1/x2 = 4/(0.2 + x)2
=> 1/x = 2/(0.2 + x)
=> 0.2 + x = 2x
=> x = 0.2 m
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