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Q.

Two charges, each equal to q, are kept at x=-a and x=a on the x-axis. A particle of mass m and charge q0=q / 2 is placed at the origin. If charge q0 is given a small displacement (y<<a) along the y-axis, the net force acting on the particle is proportional to:

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a

y

b

-1/y

c

-y

d

1/y

answer is D.

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Detailed Solution

From the figure shown here, the net force is
Fnet =2Fcos⁡θ=2×k×q×(q/2)a2+y22×ya2+y2Fnet =kq2ya3(y≪a)
From the above relation, we see that the net force is directly proportional to y.
 

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