Question

To see why an MRI utilizes iron to increase the magnetic field created by a coil, calculate the current needed in a 400-loop-per-meter circular coil 0.660 m in radius to create a 1.20-T field (typical of an MRI instrument) at its center with no iron present. The magnetic field of a proton is approximately like that of a circular current loop 0.650×10−15 m in radius carrying 1.05×104 A . What is the field at the center of such a loop?

Answer 1

To create a 1.20-T magnetic field at the center of a 400-loop-per-meter coil with a radius of 0.660 m, a current of approximately 2.30 x 10^6 Amps is needed.

Step-by-step explanation:

The magnetic field produced by a circular current loop at its center is given by the formula B = (μ₀IR²)/(2R²) where B is the magnetic field, I is the current, R is the radius of the loop, and μ₀ is the permeability of free space (4π x 10^-7 T·m/A).

Using this formula, we can calculate the current needed to create a 1.20-T field at the center of a 400-loop-per-meter circular coil with a radius of 0.660 m. Plugging in the values, we get:

B = (μ₀I)/(2R)

1.20 T = (4π x 10^-7 T·m/A)I/(2 x 0.660 m)

From this equation, we can solve for I:

I = (2 x 1.20 T x 0.660 m)/(4π x 10^-7 T·m/A)

I ≈ 2.30 x 10^6 A

Therefore, a current of approximately 2.30 x 10^6 Amps is needed.