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  4. A long straight' solid metal wire of radius 2mm caries current uniformly distributed over its circular cross section. The magnetic field induction at a distance 2mm from its axis is B . Then the maghetic field induction at a distance 1 mm from the axis will be

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Q. A long straight' solid metal wire of radius 2mm caries current uniformly distributed over its circular cross section. The magnetic field induction at a distance 2mm from its axis is B . Then the maghetic field induction at a distance 1 mm from the axis will be

Moving Charges and Magnetism

Solution:

$B \int \,dl=\mu_0\,i =\mu_0 \frac{i}{\pi\,R^2}\pi \,r^2$
$B.2 \pi\,r =\frac{\mu_0\,i.\pi\,r^2}{\pi\,R^2}$
$\Rightarrow B \,\alpha\,r$