A steady current $I$ goes through a wire loop $P Q R$ having shape of a right angle triangle with $P Q=3 x, P R=4 x$ and $Q R=5 x$. If the magnitude of the magnetic field at $P$ due to this loop is $k\left(\frac{\mu_0 I}{48 \pi x}\right)$, find the value of $k$.

Solution

Magnetic field at point $P$ due to wires $R P$ and $R Q$ is zero. Only wire $Q R$ will produce magnetic field at $P$. $$ r=3 x \cos 37^{\circ}=(3 x)\left(\frac{4}{5}\right)=\frac{12 x}{5} $$

Hence, the correct answer is 7.