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Two long wires have uniform charge density λ per unit length each. The wires are non-coplanar and mutually perpendicular. Shortest distance between them is d. The Interaction force between them is:

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a

λ22ε0

b

λ22πε0

c

2λ2ε0

d

λ24ε0

answer is A.

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Detailed Solution

F=∫dF=∫Ecosθdq=∫Ecosθλ.dy=∫λ2π∈0rcosθ λ.dy Now , yd=tanθ ⇒ dy=d.sec2θdθ Also, dr=cosθ ⇒r=d.secθ ∴F=∫dF=∫λ2π∈0dsecθcosθλ dsec2θdθ ⇒F=λ22π∈0∫−π2π2dθ=λ22∈0

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Two long wires have uniform charge density λ per unit length each. The wires are non-coplanar and mutually perpendicular. Shortest distance between them is d. The Interaction force between them is: