Question

The cross-sectional area of an adjustable single loop is reduced from 1.0 m² to 0.25 m² in 0.20s. What is the average emf that is induced in this coil if it is in a region where B = 4.0 T and the coil’s plain is perpendicular to B?

a) 12 V

b) 15 V

c) 18 V

d) 21 V

e) 24 V

Answer 1

The average induced electromotive force (emf) in the coil is 15 V, which is calculated using Faraday's law of electromagnetic induction.

Step-by-step explanation:

The student's question is about calculating the average electromotive force (emf) induced in a coil due to a change in its cross-sectional area in a magnetic field, which is a concept from the subject of Physics within the topic of electromagnetic induction.

To calculate the induced emf, we can use Faraday's law, which states that emf = - dΦ/dt, where Φ is the magnetic flux through the coil. The flux Φ is given by Φ = B × A, where B is the magnetic field strength and A is the area of the coil. In this problem, B is 4.0 T, and the area A changes from 1.0 m² to 0.25 m² in 0.20s. Thus, the change in flux dΦ is (4.0 T)(1.0 m² - 0.25 m²) = 3 Tm². The change in time dt is 0.20 s.

The average induced emf is therefore emf = - dΦ/dt = - (3 Tm² / 0.20 s) = -15 V. Since the question asks for the magnitude, we take the absolute value and get 15 V.