Rankers Physics

Magnetic Field Due to Straight Current Carrying Wire: Practice Problem & Solution

A long straight wire along the z-axis carries a current I in the negative z-direction. The magnetic vector field \[\overrightarrow{B}\] at a point having coordinates (x, y) in the z = 0 plane is :
\[\frac{\mu_{0}I}{2\pi}\left( \frac{y\hat{i}-x\hat{j}}{x^{2}+y^{2}} \right)\]
\[\frac{\mu_{0}I}{2\pi}\left( \frac{x\hat{i}+y\hat{j}}{x^{2}+y^{2}} \right)\]
\[\frac{\mu_{0}I}{2\pi}\left( \frac{x\hat{j}-y\hat{i}}{x^{2}+y^{2}} \right)\]
\[\frac{\mu_{0}I}{2\pi}\left( \frac{x\hat{i}-y\hat{j}}{x^{2}+y^{2}} \right)\]

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1. A long straight wire of radius $a$ carries a steady current $I$. The current is uniformly distributed over its cross-section. The ratio of the magnetic fields $B$ and $B'$ at radial distances $\frac{a}{2}$ and $2a$ respectively, from the axis of the wire is: (2016-1)
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