A technician wearing a brass bracelet enclosing area 0.00500 m2 places her hand in a solenoid whose magnetic field is 4.50 T directed perpendicular to the plane of the bracelet. The electrical resistance around the circumference of the bracelet is 0.0200. An unexpected power failure causes the field to drop to 1.35 T in a time of 20.0 ms. (a) Find the current induced in the bracelet.

39.375 A

Explanation:

To find the induced current, we use the relation

e = - ΔΦ/Δt, where

ΔΦ = change in magnetic flux of the bracelet

Δt = change in time, = 20 ms

Also, Φ = A.ΔB, such that

A = area of the bracelet, 0.005m²

ΔB = magnetic field strength of the bracelet = 1.35 - 4.5 = - 3.15 T

ΔΦ = A.ΔB

ΔΦ = 0.005 * - 3.15

ΔΦ = -.01575 wb

e = - ΔΦ/Δt

e = - 0.01575 / 20*10^-3

e = 0.7875 V

From the question, the resistance of the bracelet is 0.02 ohm, so

From Ohms Law, I = V/R

I = 0.7875 / 0.02

I = 39.375 A