Q.

In the figure shown an infinitely long wire of uniform linear charge density λ is kept perpendicular to the plane of figure such that it extends upto infinity on both sides of the paper. Find the electrostatic force on a semicircular ring kept such that its geometrical axis coincides with the wire. The semicircular ring has a uniform linear charge density λ.

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a

λλπε0

b

λλ4πε0

c

λλ2πε0

d

λλ'πε0R

answer is D.

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Detailed Solution

The electrostatic field intensity at a point on the ring is E =λ2πε01R.
The force on the elementary charge dq is
dF=dqE=λRdθλ2πε01R
The sine component of dF will get cancelled and cosine component will get added.
Net force on the ring
F=20+π/2dFcosθ=20+π/2λλ2πε0cosθ=λλπε0
λλπε0

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