# Find the current induced by a magnetic field, and the power

1. Nov 10, 2012

1. The problem statement, all variables and given/known data
A technician wearing a brass bracelet enclosing area 0.005 00 m2 places her hand in a solenoid whose magnetic field is 5.00 T directed perpendicular to the plane of the bracelet. The electrical resistance around the circumference of the bracelet is 0.020 0 Ω. An unexpected power failure causes the field to drop to 1.50 T in a time of 20.0 ms. Find (a) the current induced in the bracelet and (b) the power delivered to the bracelet.

2. Relevant equations
ΔB = 5.00T - 1.50T = 3.5T (which I will use)
A = 0.005 m2
R = 0.02Ω
t = 0.02s
Flux = BA
ε = Flux/t
I = ε/R
P = ε2/R

3. The attempt at a solution
Flux = 3.5T X .005m2 = 0.0175 Wb
ε = 0.0175 / 0.02s = 0.875 V
I = 0.875V / 0.02Ω = 43.75A

and

P = 0.8752/0.02 = 38.28w

My question is: Did I handle correctly the difference in Magnetic field by using 5-1.5?

2. Nov 10, 2012

### TSny

Yes. The induced emf is equal to the change in flux divided by the time interval. ε = $\Delta$ $\Phi$/$\Delta t$. So, you are correct to use the change in B to find the change in the flux.