Two particle A andBhaving charges 8.0x10-6C & -2.0x10-6C are held fixed with a separation of 20cm. Where should a third charged particle be placed so that it does not experience a net electric force?
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