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(D) Let the point $P$ be at a distance $r$ from wire $A$ where the resultant magnetic field is zero.Since the currents are in the same direction,the m

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$12.5$

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(D) Let the point $P$ be at a distance $r$ from wire $A$ where the resultant magnetic field is zero.Since the currents are in the same direction,the magnetic fields produced by the two wires at a point between them will be in opposite directions.For the resultant magnetic field to be zero at point $P$,the magnitudes of the magnetic fields produced by wires $A$ and $B$ must be equal.$B_A = B_B$$\frac{\mu_0 i_1}{2 \pi r} = \frac{\mu_0 i_2}{2 \pi (d - r)}$Where $i_1 = 12 \,A$,$i_2 = 36 \,A$,and $d = 50 \,cm = 0.5 \,m$.$\frac{12}{r} = \frac{36}{0.5 - r}$$\frac{1}{r} = \frac{3}{0.5 - r}$$0.5 - r = 3r$$4r = 0.5$$r = \frac{0.5}{4} = 0.125 \,m = 12.5 \,cm$Thus,the point is at a distance of $12.5 \,cm$ from wire $A$.

Two long parallel straight metal wires $A$ and $B$ carrying currents $12 \,A$ and $36 \,A$ respectively,in the same direction are separated by $50 \,cm$. The point relative to $A$,where the resultant magnetic induction between the two wires due to the currents is zero,will be (in $\,cm$)

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