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Two negatively charged particles of unit magnitude and charge are placed along a straight line. If charge q is placed at the midpoint between charges, then, q is in a) stable equilibrium b) unstable equilibrium c) neutral equilibrium d) none
seeassume distance between the particles -1c ans -1c is 2dthen q charge is at dassume q is positve (without loss of generality)then attr for by left -1c =kq/d^2attr. right -1c =kq=/d^2lets assume particle suffers a small diplacement of x x<<d towards right particlenow force left= kq/(d+x)^2right =kq(/d-x)^2since x<<dwe approximate the force and find difference right -left =4kqx/d^2 (1+x)^n=1+nx when x<<1which is not proportional to -xso unstable equilibirum
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