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

AI Thread Summary
The technician's brass bracelet, with an area of 0.005 m² and a resistance of 0.020 Ω, experiences a change in the magnetic field from 5.00 T to 1.50 T, resulting in a change of 3.5 T. The magnetic flux through the bracelet is calculated as 0.0175 Wb, leading to an induced electromotive force (emf) of 0.875 V over a time interval of 20.0 ms. Using Ohm's law, the induced current in the bracelet is determined to be 43.75 A. The power delivered to the bracelet is calculated to be 38.28 W. The calculations confirm the correct handling of the magnetic field change to find the induced current and power.
Parad0x88
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Homework Statement


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.


Homework 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


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?
 
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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.
 
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