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(C) The direction of the magnetic field $(B_1, B_2, B_3, B_4)$ at the origin due to wires $1, 2, 3,$ and $4$ is shown in the figure.For each wire,the

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$2\sqrt{2} \,B$

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(C) The direction of the magnetic field $(B_1, B_2, B_3, B_4)$ at the origin due to wires $1, 2, 3,$ and $4$ is shown in the figure.For each wire,the magnitude of the magnetic field at the origin is given by $B = \frac{\mu_0}{4\pi} \cdot \frac{2i}{x}$.By applying the right-hand rule:- Wire $1$ (current out of page) produces $B_1$ in the $+x$ direction.- Wire $2$ (current into page) produces $B_2$ in the $+y$ direction.- Wire $3$ (current into page) produces $B_3$ in the $+x$ direction.- Wire $4$ (current out of page) produces $B_4$ in the $+y$ direction.Thus,the total magnetic field components are:$B_x = B_1 + B_3 = B + B = 2B$$B_y = B_2 + B_4 = B + B = 2B$The resultant magnetic field at the origin is:$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$.

What will be the resultant magnetic field at the origin due to four infinite length wires? If each wire produces a magnetic field '$B$' at the origin.

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