Two concentric circular loops of wire lie on a tabletop, one inside the other. The inner wire has a diameter of 20.0 cm and carries a clockwise current of 12.0 A, as viewed from above, and the outer wire has a diameter of 30.0 cm. What must be the magnitude and direction (as viewed from above) of the current in the outer wire so that the net magnetic field due to this combination of wires is zero at the common center of the wires?

Question

Physics

Rabbit

19 September, 03:07

Two concentric circular loops of wire lie on a tabletop, one inside the other. The inner wire has a diameter of 20.0 cm and carries a clockwise current of 12.0 A, as viewed from above, and the outer wire has a diameter of 30.0 cm. What must be the magnitude and direction (as viewed from above) of the current in the outer wire so that the net magnetic field due to this combination of wires is zero at the common center of the wires?

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Amari Graves · Answer 1

Magnetic field due to circular wire at the center = μ₀ I / 2 r

I is current and r is radius. μ₀ = 4π x 10⁻⁷.

field B₁ due to inner loop

B₁ = 4π x 10⁻⁷ x 12 / 2 x. 20

= 376.8 x 10⁻⁷

Field due to outer loop

B₂ = 4π x 10⁻⁷ x I / 2 x. 30

For equilibrium

B₁ = B₂

376.8 x 10⁻⁷ = 4π x 10⁻⁷ x I / 2 x. 30

I = 18 A.

The direction should be opposite to that in the inner wire. It should be anti-clockwise.