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Q. The magnetic field at $P$ on the axis of a solenoid having $100$ turn/ $m$ and carrying a current of $5\, A$ isPhysics Question Image

AIIMSAIIMS 2011

Solution:

The magnetic field at $P$ is
$B=\frac{\mu_{0} n I}{2}(\cos \theta+\cos \theta)$
where $n$ is number of turns, $I$ the current.
Given, $n=100, I=5 A$ and $\theta=45^{\circ}$
$\therefore B=\frac{\mu_{0} \times 100 \times 5}{2} \times \frac{2}{\sqrt{2}}$
$\Rightarrow B =250 \sqrt{2} \,\mu_{0}$