At what distance from wire 'B' does the magne | vedclass

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(C) Let the point where the magnetic field is zero be at a distance '$x$' from wire '$A$' and distance '$(6 - x)$' from wire '$B$'.Since both wires ca

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$\frac{12}{7} \, cm$

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(C) Let the point where the magnetic field is zero be at a distance '$x$' from wire '$A$' and distance '$(6 - x)$' from wire '$B$'.Since both wires carry current in the same direction,the null point lies between them.The magnetic field due to a long straight wire is given by $B = \frac{\mu_0 I}{2\pi r}$.For the net magnetic field to be zero at point $P$,the magnitudes of the magnetic fields produced by wire '$A$' and wire '$B$' must be equal:$\frac{\mu_0 (5i)}{2\pi x} = \frac{\mu_0 (2i)}{2\pi (6 - x)}$$\frac{5}{x} = \frac{2}{6 - x}$$5(6 - x) = 2x$$30 - 5x = 2x$$7x = 30$$x = \frac{30}{7} \, cm$ (distance from wire '$A$').The distance from wire '$B$' is $(6 - x) = 6 - \frac{30}{7} = \frac{42 - 30}{7} = \frac{12}{7} \, cm$.

At what distance from wire '$B$' does the magnetic field become zero?

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