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(C) The magnetic field produced by an infinitely long straight wire at a distance $r$ is given by $B = \frac{\mu_{0} i}{2 \pi r}$.Let $i_{1} = 10 \ A$

Vedclass · Accepted Answer

$30$

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(C) The magnetic field produced by an infinitely long straight wire at a distance $r$ is given by $B = \frac{\mu_{0} i}{2 \pi r}$.Let $i_{1} = 10 \ A$ be the current in wire $1$ and $i_{2} = I$ be the current in wire $2$.The distance of point $A$ from wire $1$ is $r_{1} = 9 \ cm$.The distance of point $A$ from wire $2$ is $r_{2} = 18 \ cm + 9 \ cm = 27 \ cm$.For the resultant magnetic field at $A$ to be zero,the magnetic fields produced by the two wires must be equal in magnitude and opposite in direction.$B_{1} = B_{2}$$\frac{\mu_{0} i_{1}}{2 \pi r_{1}} = \frac{\mu_{0} i_{2}}{2 \pi r_{2}}$$\frac{i_{1}}{r_{1}} = \frac{i_{2}}{r_{2}}$Substituting the values: $\frac{10}{9} = \frac{I}{27}$$I = \frac{10 	imes 27}{9} = 30 \ A$.

In the figure,two parallel infinitely long current-carrying wires are shown. If the resultant magnetic field at point $A$ is zero,then determine the current $I$ (in $A$).

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