Find the electric flux crossing the wire frame ABCD of length l, width b, and center at a distance OP=d from an infinite line of charge with linear charge density λ. Consider that the plane of the frame is perpendicular to the line OP Fig.
Nπε0tan−1(b2d)
3Nπε0tan−1(7b2d)
2Nπε0tan−1(b2d)
N2πε0tan−1(b2d)
A
Nπε0tan−1(b2d)
B
2Nπε0tan−1(b2d)
C
3Nπε0tan−1(7b2d)
D
N2πε0tan−1(b2d)
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Solution
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The flux passing through the strip of area dA is dϕ=EdAcosθ
=λ2πε0√d2+x2(ldx)d√d2+x2
dϕ=λdl2πε0d(√d2+x2)
∴ϕ=∫dϕ=λdl2πε0∫b/2−b/2dd2+x2
=λdl2πε01d[tan−1xd]b/2−b/2
=N2πε0×2tan−1(b2d)
ϕ=N2πε0tan−1(b2d)
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