Magnetics 6 Question 23
26. 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 $k \frac{\mu _0 I}{48 \pi x}$,find the value of $k$.
(2009)
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Answer:
Correct Answer: 26. 7
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 $P$.
$$ r=3 x \cos 37^{\circ}=(3 x) \frac{4}{5}=\frac{12 x}{5} $$
Now,
$$ \begin{aligned} B & =\frac{\mu _0}{4 \pi} \frac{I}{12 x / 5} \quad\left[\sin 37^{\circ}+\sin 53^{\circ}\right] \\ & =7 \frac{\mu _0 I}{48 \pi x} \end{aligned} $$
