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Q.

Equal current i is flowing in two parallel conductors, distant 2 l, in mutually opposite directions as shown in fig. The magnetic induction at a point P equidistant r from both conductors will be

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a

$\frac{μ_{0} il}{{πr}^{2}}$

b

$\frac{μ_{0} il}{πr}$

c

$\frac{μ_{0} {il}^{2}}{{πr}^{2}}$

d

$\frac{μ_{0} {il}^{2}}{πr}$

answer is A.

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Detailed Solution

See fig. The resultant magnetic field at P will be

Question Image

$\begin{aligned} B^{'} = 2 Bsin θ \\ = 2 (\frac{μ_{0} i}{2 πr}) \frac{l}{r} = \frac{μ_{0} il}{{πr}^{2}} \end{aligned}$

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Equal current i is flowing in two parallel conductors, distant 2 l, in mutually opposite directions as shown in fig. The magnetic induction at a point P equidistant r from both conductors will be