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(C) The magnitude of the magnetic field produced by each wire at the origin is given as $B = \frac{\mu_0}{2\pi x} i$.Using the right-hand rule,we dete

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$2\sqrt{2}\, B$

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(C) The magnitude of the magnetic field produced by each wire at the origin is given as $B = \frac{\mu_0}{2\pi x} i$.Using the right-hand rule,we determine the direction of the magnetic field due to each wire at the origin:- Wire $1$ (current out of page): Field $B_1$ is in the $+x$ direction.- Wire $2$ (current into page): Field $B_2$ is in the $+y$ direction.- Wire $3$ (current into page): Field $B_3$ is in the $+x$ direction.- Wire $4$ (current out of page): Field $B_4$ is in the $+y$ direction.Summing the fields along each axis:$B_x = B_1 + B_3 = B + B = 2B$$B_y = B_2 + B_4 = B + B = 2B$The resultant magnetic field is $B_{net} = \sqrt{B_x^2 + B_y^2} = \sqrt{(2B)^2 + (2B)^2} = \sqrt{4B^2 + 4B^2} = \sqrt{8B^2} = 2\sqrt{2}B$.

Find the resultant magnetic field at the origin due to four infinitely long wires. Each wire produces a magnetic field of magnitude $B$ at the origin.

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