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  4. A long straight wire of a circular cross section (radius a ) carries a steady current I and the current I is uniformly distributed across this cross-section. Which of the following plots represents the variation of magnitude of magnetic field B with distance r from the centre of the wire?

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Q. A long straight wire of a circular cross section (radius $a$ ) carries a steady current $I$ and the current $I$ is uniformly distributed across this cross-section. Which of the following plots represents the variation of magnitude of magnetic field $B$ with distance $r$ from the centre of the wire?

Moving Charges and Magnetism

Solution:

Magnetic field due to a long straight wire of radius $a$ carrying current $I$ at a point distant $r$ from the centre of the wire is given as follows:
$B=\frac{\mu_{0} I r}{2 \pi a^{2}}$ for $r<\,a $
$B=\frac{\mu_{0} I}{2 \pi a}$ for $ r=a $
$B=\frac{\mu_{0} I}{2 \pi r} $ for $ r>\,a$
image
The variation of magnetic field $B$ with distance $r$ from the centre of wire is shown in the figure.