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Q.

Two parallel wires carrying equal currents in opposite directions are placed at x = ±a parallel to y-axis with z = 0. Magnetic field at origin O is B₁ and at P (2a, 0, 0) is B₂. Then, the ratio B₁/B₂ is

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a

3

b

1/2

c

1/3

d

2

answer is A.

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Detailed Solution

As shown in figure,

${\vec{B}}_{1} = - 2 (\frac{μ_{0}}{2 π} \frac{i}{a}) \hat{k} = - \frac{μ_{0} i}{π a} \hat{k}$

= Magnetic field at O

${\vec{B}}_{2} = \frac{μ_{0}}{2 π} \frac{i}{a} \hat{k} - \frac{μ_{0}}{2 π} \frac{i}{3 a} \hat{k} = \frac{μ_{0}}{3 π} \frac{i}{a} \hat{k}$

= Magnetic field at P

Question Image

$∴ B_{1} / B_{2} = 3$

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Two parallel wires carrying equal currents in opposite directions are placed at x = ±a parallel to y-axis with z = 0. Magnetic field at origin O is B1 and at P (2a, 0, 0) is B2. Then, the ratio B1/B2 is