NEET 2022 — Physics solution

NEET2022Physics

From Ampere's circuital law for a long straight wire of circular cross-section carrying a steady current, the variation of magnetic field in the inside and outside region of the wire is:

A
a linearly increasing function of distance upto the boundary of the wire and then linearly decreasing for the outside region.
B
a linearly increasing function of distance r upto the boundary of the wire and then decreasing one with 1/r dependence for the outside region.
C
a linearly decreasing function of distance upto the boundary of the wire and then a linearly increasing one for the outside region.
D
uniform and remains constant for both the regions.

Solution

For a long straight wire of radius $R$ carrying current $I$ uniformly distributed across its cross-section, apply Ampere's law to a circular loop of radius $r$ coaxial with the wire.

Inside ( $r < R$ ): enclosed current scales as $r^{2}$ , giving $B = \frac{μ _{0} I r}{2 π R ^{2}}$ , linear in $r$ .

Outside ( $r > R$ ): enclosed current is $I$ , giving $B = \frac{μ _{0} I}{2 π r}$ , falling as $1/ r$ .

So $B$ rises linearly up to $r = R$ and then decays as $1/ r$ outside.

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