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(C) The magnetic field $B$ at a distance $r$ from an infinite straight wire carrying current $I$ is given by $B = \frac{\mu_0 I}{2 \pi r}$.For the wir

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$I\left(\frac{y}{x+y}\right)$

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(C) The magnetic field $B$ at a distance $r$ from an infinite straight wire carrying current $I$ is given by $B = \frac{\mu_0 I}{2 \pi r}$.For the wire carrying current $I$ (upward), the magnetic field at point $P$ (at a distance $x+y$ from it) is directed into the plane (downward) and its magnitude is $B_I = \frac{\mu_0 I}{2 \pi (x+y)}$.For the wire carrying current $i$ (downward), the magnetic field at point $P$ (at a distance $y$ from it) is directed out of the plane (upward) and its magnitude is $B_i = \frac{\mu_0 i}{2 \pi y}$.Since the net magnetic field at point $P$ is zero, the magnitudes of the magnetic fields must be equal:$B_I = B_i$$\frac{\mu_0 I}{2 \pi (x+y)} = \frac{\mu_0 i}{2 \pi y}$$\frac{I}{x+y} = \frac{i}{y}$$i = I \left( \frac{y}{x+y} \right)$

Two infinite wires carrying opposite electrical currents $I$ and $i$ are placed a distance $x$ apart. $A$ point $P$ at a distance $y$ away from the wire carrying current $i$ is shown in the figure. If the magnetic field is zero at point $P$, then the magnitude of $i$ is

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