A technician wearing a brass bracelet enclosing area 0.00500 m^2 places her hand

Question

A technician wearing a brass bracelet enclosing area 0.00500 m^2 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 fi. An unexpected power failure causes the field to drop to 1.35 T in a time of 18.0 ms. Find the current induced in the bracelet. Find the power (3r) delivered to the bracelet. (As this problem implies, you should not wear any metal objects when working in regions of strong magnetic fields.)

Explanation / Answer

Part a)

This problem can solve it with the use of Faraday's law

E = - dB /dt

B = B . A = B A Cos

= 0 since the solenoid axis and the normal to the bracelet are parallel

Data

A = 0.00500 m²

B1= 4.50 T

B2 =1.35 T

t =18.0 ms = 18.0 10-3 s

E = - A dB/dt

dB/dt = (4.50 -1.35)/ 18 10-3

dB/dt = 1.75 102 T/s

E = - 0.005 1.75 102

There is an error in the multiplication and fix it and this is the correct value

E = - 0.875 V

We calculate the current

E= I R

I =E/R

I= 0.875 /0.0200

I= -43.75 A

Part b)

P = V I

P = - 0.875 (-43.75 )

P = 38.28 W

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