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Question: Two mutually perpendicular infinitely long lines of charge having charge per unit length as l<sub>1<...

Two mutually perpendicular infinitely long lines of charge having charge per unit length as l1 and l2 are located in air at a distance "a" from each other. The force of interaction between them is–

A

λ1λ24ε0\frac{\lambda_{1}\lambda_{2}}{4\varepsilon_{0}}

B

λ1λ22aε0\frac{\lambda_{1}\lambda_{2}}{2a\varepsilon_{0}}

C

λ1λ22ε0\frac{\lambda_{1}\lambda_{2}}{2\varepsilon_{0}}

D

λ1λ24aε0\frac{\lambda_{1}\lambda_{2}}{4a\varepsilon_{0}}

Answer

λ1λ22ε0\frac{\lambda_{1}\lambda_{2}}{2\varepsilon_{0}}

Explanation

Solution

dF = λ2×λ12πε0a2+y2.dy\frac { \lambda _ { 2 } \times \lambda _ { 1 } } { 2 \pi \varepsilon _ { 0 } \sqrt { \mathrm { a } ^ { 2 } + \mathrm { y } ^ { 2 } } } . \mathrm { dy }

dFx = dF cos q

and Fx = ∫−∞+∞dFx\int _ { - \infty } ^ { + \infty } \mathrm { dF } _ { \mathrm { x } }