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Question

A long straight wire of radius R carries a steady current $$I_o$$, uniformly distributed throughout the cross-section of the wire. The magnetic field at a radial distance r from the centre of the wire, in the region $$r > R$$, is?

A
$$\dfrac{\mu_oI_o}{2\pi r}$$
B
$$\dfrac{\mu_oI_oR^2}{2\pi r}$$
C
$$\dfrac{\mu_oI_or^2}{2\pi R}$$
D
$$\dfrac{\mu_oI_o}{2\pi R}$$
E
$$\dfrac{\mu_oI_or^2}{2\pi R^2}$$
Solution
Verified by Toppr

Correct option is A. $$\dfrac{\mu_oI_o}{2\pi r}$$
Radius of wire$$=$$R
Steady current passing through the wire$$=I_o$$
The magnetic field at radial distance r from the centre of the wire
$$\displaystyle\oint B\cdot dl=\mu_oi$$
$$\Rightarrow B\displaystyle\int dl=\mu_oI_o$$
$$\Rightarrow B=\dfrac{\mu_oI_o}{2\pi r}$$.

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