An MRI technician moves his hand from a region of very low magnetic field strength into an MRI scanner's 1.80 T field with his fingers pointing in the direction of the field. His wedding ring has a diameter of 2.23 cm, and it takes 0.320 s to move it into the field.

1. What average current is induced in the ring in A if its resistance is 0.0100 Ω?

2. What average power is dissipated in mW?

3. What magnetic field is induced at the center of the ring in T?

Given that,

Magnetic field strength is

B = 1.8T

The wedding ring has a diameter of

d = 2.23 cm = 0.023m

Time take t = 0.32 secs

A. Current induced

From ohms law

V= iR, given that R = 0.01Ω

So, we need to get the induced emf

Using

ε = -NdΦ / dt

Where Φ = BA

ε = -A ∆B / ∆t

ε = -¼πd²(B2-B1) / (t2-t1)

ε = -¼ × π × 0.023² × -1.8 / 0.32

ε = 0.0023371 V

Then

I = ε / R

I = 0.002337 / 0.01

I =0.2337 A

B. Power discippated?

Power is given as

P = iV

P = 0.2337 × 0.002337

P = 0.0005462 W

P = 0.56 mW

C. The magnetic field at the centre of the ring.

The electric field at the centre of the ring is zero because each part of the ring will cause a symmetrical opposite magnitude at every point,

Then, B = 0 T

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