SATHEE: Magnetics 6 Question 23

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 $k \frac{μ_{0} I}{48 π x}$ ,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,

$\begin{aligned} B & = \frac{μ_{0}}{4 π} \frac{I}{12 x / 5} [\sin 37^{\circ} + \sin 53^{\circ}] \\ = 7 \frac{μ_{0} I}{48 π x} \end{aligned}$

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Magnetics 6 Question 23

26. A steady current I goes through a wire loop PQR having shape of a right angle triangle with PQ=3x,PR=4x and QR=5x. If the magnitude of the magnetic field at P due to this loop is kμ0I48πx,find the value of k.

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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 $k \frac{μ_{0} I}{48 π x}$ ,find the value of $k$ .