GATE EC 2012 Electromagnetics Solution Q 8

# GATE EC 2012 Electromagnetics Solution Q 8

An infinitely long uniform solid wire of radius a carries a uniform dc current of density \overrightarrow j

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

a)

r\;for\;r\;\;a

b)

0\;for\;r\;\;a

c)

r\;for\;r\;a

d)

0\;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)

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

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