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A current of I amperes is flowing through each of the bent wires as shown. Find the magnitude of magnetic field at O.

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$\frac{μ_{0} I}{2 R}$

$(\frac{μ_{0} I}{2 R} + \frac{3 μ_{0} I}{4 R^{1}})$

$(\frac{μ_{0} I}{8 R} + \frac{3 μ_{0} I}{8 R^{1}})$

$(\frac{μ_{0} I}{2 R} + \frac{μ_{0} I}{2 R^{1}})$

answer is A.

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Detailed Solution

$B_{n e t} = B + B^{'}$

$= \frac{1}{4} . \frac{μ_{0} i}{2 R} + \frac{3}{4} . \frac{μ_{0} i}{2 R^{1}}$

$= \frac{μ_{0} i}{8 R} + \frac{3 μ_{0} i}{8 R^{1}}$

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