In the figure,two parallel infinitely long cu | vedclass

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

Vedclass · Accepted Answer

$30$

Vedclass · Answer

(C) The magnetic field due to an infinitely long straight wire at a distance $r$ is given by $B = \frac{\mu_{0} I}{2 \pi r}$.Let $I_{1} = 10 	ext{ A}$ be the current in the right wire and $I_{2} = I$ be the current in the left wire.The distance of point $A$ from the right wire is $r_{1} = 9 	ext{ cm}$.The distance of point $A$ from the left wire is $r_{2} = 18 	ext{ cm} + 9 	ext{ cm} = 27 	ext{ cm}$.For the resultant magnetic field at point $A$ to be zero,the magnitudes of the magnetic fields produced by both wires must be equal,i.e.,$B_{1} = B_{2}$.$\frac{\mu_{0} I_{1}}{2 \pi r_{1}} = \frac{\mu_{0} I_{2}}{2 \pi r_{2}}$$\frac{10}{9} = \frac{I}{27}$$I = \frac{10 	imes 27}{9} = 30 	ext{ 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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