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

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SUMMARY

The discussion focuses on calculating the induced current and power in a brass bracelet subjected to a changing magnetic field within a solenoid. The technician's bracelet, with an area of 0.005 m² and a resistance of 0.020 Ω, experiences a magnetic field change from 5.00 T to 1.50 T over 20.0 ms. The induced electromotive force (emf) is calculated to be 0.875 V, resulting in an induced current of 43.75 A and a power delivery of 38.28 W. The calculations confirm the correct application of Faraday's law of electromagnetic induction.

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  • Understanding of Faraday's law of electromagnetic induction
  • Knowledge of calculating magnetic flux
  • Familiarity with Ohm's law
  • Basic concepts of electrical power calculations
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Students in physics, electrical engineers, and professionals involved in electromagnetic applications will benefit from this discussion, particularly those focusing on induced currents and power calculations in magnetic fields.

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 = [itex]\Delta[/itex] [itex]\Phi[/itex]/[itex]\Delta t[/itex]. So, you are correct to use the change in B to find the change in the flux.
 

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