A thin,straight conductor lies along the axis | vedclass

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(B) Let the current in the thin conductor be $I$ and the current in the hollow conductor be $I$. Both currents are in the same direction.For $r < R$,t

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(B) Let the current in the thin conductor be $I$ and the current in the hollow conductor be $I$. Both currents are in the same direction.For $r For $r > R$,the total current enclosed by an Amperian loop of radius $r$ is $I + I = 2I$. Using Ampere's circuital law,$B(2\pi r) = \mu_0 (2I)$,so $B = \frac{\mu_0 (2I)}{2\pi r} = \frac{\mu_0 I}{\pi r}$. Thus,$B \propto \frac{1}{r}$.At $r = R$,the magnetic field due to the hollow conductor is zero inside $(r  R)$,the field is the sum of the fields from both conductors,which is $\frac{\mu_0 I}{2\pi R} + \frac{\mu_0 I}{2\pi R} = \frac{\mu_0 I}{\pi R}$.Therefore,the magnetic field $B$ jumps from $\frac{\mu_0 I}{2\pi R}$ to $\frac{\mu_0 I}{\pi R}$ at $r = R$,and follows a $1/r$ dependence in both regions. This corresponds to the graph where there is a discontinuous jump at $r = R$ and both segments follow a $1/r$ curve.

$A$ thin,straight conductor lies along the axis of a hollow conductor of radius $R$. The two carry equal currents in the same direction. The magnetic field $B$ is plotted against the distance $r$ from the axis. Which of the following best represents the resulting curve?

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