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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 = 4x and QR = 5x. 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.

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answer is 7.

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Detailed Solution

Below figure shows the situation described in question
Question Image
Here $d = 4 x \cos 37^{0} = 4 x \times \frac{3}{5}$
Magnitude of magnetic field at P is given as
$B_{p} = \frac{μ_{0} I}{4 π d} [\sin 37^{0} + \sin 53^{0}] \Rightarrow B_{p} = \frac{μ_{0} I}{4 π \frac{12 x}{5}} [\frac{7}{5}] = \frac{7}{48} \frac{μ_{0} I}{π x} \Rightarrow B_{p} = 7 (\frac{μ_{0} I}{48 π x}) \Rightarrow K = 7$

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