What will be the resultant magnetic field at origin due to four infinite length wires. If each wire produces magnetic field '$B$' at origin
Diffcult
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(c) Direction of magnetic field ($B_1, B_2, B_3\, and \,B_4$) at origin due to wires $1$, $2$, $3$ and $4$ are shown in the following figure.
${B_1} = {B_2} = {B_3} = {B_4} = \frac{{{\mu _0}}}{{4\pi }}.\frac{{2i}}{x} = B$. So net magnetic field at origin $O$
${B_{net}} = \sqrt {{{({B_1} + {B_3})}^2} + {{({B_2} + {B_4})}^2}} $$ = \sqrt {{{(2B)}^2} + {{(2B)}^2}} = 2\sqrt 2 \,B$
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