A steady current $I$ goes through a wire loop $PQR$ having shape of a right angle triangle with $PQ = 3x,\ PR = 4\ x$ and $QR = 5x$. 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 $k$

Question

Dr. Abubacker · Accepted Answer

(c) Magnetic field at $P$ due to $PQ\ \&\ PR$ is zero
$	herefore$ Magnetic field at $P$ due to $QR$
$B = \frac{\mu_{0}}{4\pi} \bullet \frac{I}{PS}\left( \sin\alpha + \sin\beta ight)$
Where, $B = \frac{\mu_{0}}{4\pi} \bullet \frac{1}{\frac{12x}{5}}\left\lbrack \frac{3}{5} + \frac{4}{5} ightbrack$
$B = \frac{\mu_{0}}{4\pi} 	imes \frac{1}{12x} 	imes 7 = \frac{7\mu_{0}I}{48\ \pi x}\ 	herefore k = 7$
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Q. A steady current $I$ goes through a wire loop $PQR$ having shape of a right angle triangle with $PQ = 3x,\ PR = 4\ x$ and $QR = 5x$. 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 $k$

Explanation

Reviewed by Dr. Abubacker

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