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

Step-by-step 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* 10^(-3)\ s`

The expression for the induced emf is given by :

`\epsilon=-(d\phi)/(dt)`

`\phi` = magnetic flux

`\epsilon=-(d(BA))/(dt)`

`\epsilon=-A(d(B))/(dt)`

`\epsilon=-A(B_f-B_i)/(t)`

`\epsilon=-0.005 * (0.93-3.1)/(16* 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=(V)/(R)`

`I=(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.