GATE EC 2012 Electromagnetics Solution Q 1

GATE EC 2012 Electromagnetics Solution Q 1

The magnetic field at a distance r from the center of the wire is proportional to

a) r\;for\;r\;<\;a\;and\;1/r^2\;for\;r\;>\;a

b) 0\;for\;r\;<\;a\;and\;1/r\;for\;r\;>\;a

c) r\;for\;r\;<\;a\;and\;1/r\;for\;r\;>a

d) 0\;for\;r\;<\;a\;and\;1/r^2\;for\;r\;>\;a

Ans- c)

Explanation

We know that magnetic flux density at a distance r greater than radius of wire (i.e. r > R) from the wire is,

\left|B\right|=\frac{\mu_0I}{2\pi r}

i.e.  B\propto\frac1r

For a point inside the wire (i.e. r < R)

GATE EC 2012 Electromagnetics Solution img1 - Grad Plus

In our case, \left|B\right|=\frac{\mu_0rI}{2\pi a^2}\;i.e.\;B\propto r

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