Question

Two round concentric metal wires lie on a tabletop, one inside the other. The inner wire has a diameter of 19.0 cmcm and carries a clockwise current of 20.0 AA , as viewed from above, and the outer wire has a diameter of 38.0 cmcm .What must be the 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? What must be the magnitude 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?

Answer 1

Step-by-step explanation:

magnetic field due to circular wire

= μ₀ i / 2r

i is current and r is radius of coil .

Magnetic fields due to inner coil

μ₀ x 20 / (2 x 9.5 x 10⁻²)

Magnetic field due to outer coil

= μ₀ x I / (2 x 19 x 10⁻²) , I is the current to be calculated

Total field

μ₀ x 20 /( 2 x 9.5 x 10⁻²) +μ₀ x I / (2 x 19 x 10⁻²) = 0

20 + I /2 = 0

I = - 40 A

Current required is 40 A , and it will be in opposite direction.