Question

An MRI technician moves his hand from a region of very low magnetic field strength into an MRI scanner's 2.00 T field with his fingers pointing in the direction of the field. His wedding ring has a diameter of 2.5 cm and it takes 0.45 s to move it into the field. What average current is induced in the ring in A if its resistance is 0.0100 Ω ?

Answer 1

Answer:

2.62 A

Explanation:

B = 2 T, Diameter = 2.5 cm , radius, r = 0.0125 m, t = 0.45 s, r = 0.01 ohm

Induced emf, e = rate of change of magnetic flux

e = A x dB / dt = 3.14 x (0.0125)^2 x 2 / 0.45

e = 0.026 V

induced current, i = e / R = 0.026 / 0.01 = 2.62 A

Answer 2

The average induced current in the loop is 0.218 A.

Induced emf in the loop

The emf induced in the loop is determined by applying Faraday's law as shown below;

emf = dФ/dt

emf = BA/t

where;

A is the area

A = πr² = πd²/4

A = π x (0.025)²/4

A = 4.908 x 10⁻³ m²

emf = (2 x 4.908 x 10⁻³)/(0.45)

emf = 2.18 x  10⁻³ V

Average induced current

The average induced current in the loop is calculated as follows;

I = emf/R

I = 2.18 x  10⁻³/0.01

I = 0.218 A

Learn more about induced emf here: https://brainly.com/question/13744192