Question

The tokomak reactor at Moon Base Universirty announced last week that it had achieved the highest power, fusion reaction in history. The tokomak is a toroidal coil configuration (current carrying wires wrapped around a doughnut) that achieves plasma confinement by generating a strong magnetic field. Assume that the inner radius of the toroid is 90.0 cm and that its outer radius is 110.0 cm. Assume that there are 1000 turns of superconducting wire wrapped around the toroid.

a. For what value of the current I in the wire will the magnetic induction field along the center of the toroid be 10.0 Tesla.

Answer 1

To determine the current required to achieve a magnetic induction field of 10.0 Tesla along the center of the tokamak toroid, we can use Ampere's Law. By substituting the given values into the equation, we find that the current required is 0.005 Amps.

Step-by-step explanation:

To determine the current required to achieve a magnetic induction field of 10.0 Tesla along the center of the tokamak toroid, we can use Ampere's Law.

Ampere's Law states that the line integral of the magnetic field around a closed loop is equal to the product of the current passing through the loop and the number of turns of wire.

The equation for Ampere's Law is B x 2πr = μ0 x I x N, where B is the magnetic field, r is the radius of the loop, μ0 is the permeability of free space, I is the current, and N is the number of turns of wire.

In this case, the magnetic field B is given as 10.0 Tesla, the radius of the toroid is the average of the inner and outer radii, which is (90.0 cm + 110.0 cm)/2 = 100.0 cm, and the number of turns of wire is given as 1000.

Let's substitute these values into the equation and solve for I:

B x 2πr = μ0 x I x N

10.0 Tesla x 2π x 100.0 cm = (4π x 10^-7 T m/A) x I x 1000

2000π cm*Tesla = (4π x 10^-7 T m/A) x I x 1000

2000 x 10^-2 m^2*Tesla = 4π x 10^-7 T m/A x I x 1000

5π x 10^-12 m^2*Tesla = π x 10^-3 T m/A x I

5 x 10^-12 = 10^-3 x I

I = (5 x 10^-12)/10^-3

I = 0.005 Amps

Therefore, the current required to achieve a magnetic induction field of 10.0 Tesla is 0.005 Amps.