12) A technician wearing a brass bracelet enclosing area0.00500 m 2 places her h

Question

12) A technician wearing a brass bracelet enclosing area0.00500 m2 places her hand in a solenoid whose magneticfield is 2.90 T directed perpendicular tothe plane of the bracelet. The electrical resistance around thecircumference of the bracelet is 0.0200 . An unexpectedpower failure causes the field to drop to 0.87 T in a time of 20.0 ms. (a) Find the current induced in thebracelet.
A

(b) Find the power (P) delivered to the bracelet. (Note:As this problem implies, you should not wear any metal objects whenworking in regions of strong magnetic fields.)
W (a) Find the current induced in thebracelet.
A

(b) Find the power (P) delivered to the bracelet. (Note:As this problem implies, you should not wear any metal objects whenworking in regions of strong magnetic fields.)
W

Explanation / Answer

Area A = 0.005 m ^ 2

Initial Magnetic field B = 2.9 T

Final magnetic field B ‘ = 0.87 T

Chang ein magnetic field dB = B – B’ = 2.03 T

Time interval dt = 20 ms = 0.02 s

Resistance R = 0.02 ohm

Induced emf E = A dB / dt

                        = 0.5075 Volt

Induced current I = E / R

                            = 25.375 A

(b). Power P = I ^ 2 R

                    = 12.87 W

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