Question

a 10-turn circular loop with a radius of 50 cm sits in a magnetic field that increases from 0.5 T 2.5 T. If 0.157V are induced in the wire, how quickly does the magnetic field change? (Round your answer to the nearest tenth of a second.)

Answer 1

The time taken for the magnetic field to change to the given magnitude is 100.0 s.

Induced emf in the loop

The concept of induced emf in the loop can be used to determine the rate at which the magnetic field is changing.

$emf =N\frac{d\phi}{dt}$

where;

• Ф is magnetic flux
• N is number of turns

Ф = BA

where;

A is area of the loop

A = πr²

A = π(0.5)² = 0.785 m²

$emf = N\frac{dBA}{dt} \\\\emf = NA(\frac{B_2 - B_1}{t} )\\\\t = \frac{NA(B_2 - B_1)}{emf}$

Time of change of emf

$t = \frac{10 \times 0.785 \times (2.5 - 0.5)}{0.157} \\\\t = 100.0 \ s$

Thus, the time taken for the magnetic field to change to the given magnitude is 100.0 s.

Learn more about induced emf here: https://brainly.com/question/13744192