Question

A technician wearing a brass bracelet enclosing area 0.00500 m2 places her hand in a solenoid whose magnetic field is 3.10 T directed perpendicular to the plane of the bracelet. The electrical resistance around the circumference of the bracelet is 0.0200 . An unexpected power failure causes the field to drop to 0.93 T in a time of 16.0 ms.

Answer 1

Explanation:

Given that,

Area enclosed by a brass bracelet, $A=0.005\ m^2$

Initial magnetic field, $B_i=3.1\ T$

The electrical resistance around the circumference of the bracelet is, R = 0.02 ohms

Final magnetic field, $B_f=0.93\ T$

Time, $t=16\ ms=16\times 10^{-3}\ s$

The expression for the induced emf is given by :

$\epsilon=-\dfrac{d\phi}{dt}$

$\phi$ = magnetic flux

$\epsilon=-\dfrac{d(BA)}{dt}$

$\epsilon=-A\dfrac{d(B)}{dt}$

$\epsilon=-A\dfrac{B_f-B_i}{t}$

$\epsilon=-0.005 \times \dfrac{0.93-3.1}{16\times 10^{-3}}$

$\epsilon=0.678\ volts$

So, the induced emf in the bracelet is 0.678 volts.

Using ohm's law to find the induced current as :

V = IR

$I=\dfrac{V}{R}$

$I=\dfrac{0.678}{0.02}$

I = 33.9 A

or

I = 34 A

So, the induced current in the bracelet is 34 A. Hence, this is the required solution.