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Q.

A current ‘i’ flows along an infinitely long straight conductor. If r is the perpendicular distance of a point, very far from the ends of the conductor then the magnetic induction B is given by

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a

$B = \frac{μ_{0}}{4 π} \frac{π i}{r}$

b

$B = \frac{μ_{0}}{4 π} \frac{2 i}{r}$

c

$B = \frac{μ_{0}}{4 π} \frac{i}{r}$

d

$B = \frac{μ_{0}}{4 π} \frac{2 π i}{r}$

answer is A.

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Detailed Solution

On considering an Ampere loop around the wire at a distance of r

using Ampere's law

$B (2 πr) = μ_{0} I \Rightarrow B = \frac{μ_{0} I}{2 πr}$

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A current ‘i’ flows along an infinitely long straight conductor. If r is the perpendicular distance of a point, very far from the ends of the conductor then the magnetic induction B is given by