Question

A stiff wire bent into a semicircle of radius a is rotated with a frequency f in a uniform magnetic field, as suggested in Fig. 34-51. What are (a) the frequency and (b) the amplitude of the emf induced in the loop

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

a)  58 Hz b) 7.73 mV

Explanation:

From the complete question we are given that

Radius of the semi circle , a = 3.0 cm = (3.0)(1 × $10^{-2}$ m/1 cm)

                                                              =3.0 × $10^{-2}$ m

Angular speed ,w = 58 rev/s

                             = (58 rev/s)(2π rad /1 rev)

                             = 364.4 rad/s

Magnetic field, B = 15 mT

                             = (15 mT)(1 × $10^{-3}$ T/ 1 mT)

                             = 15 × $10^{-3}$ T

a)          f = 58 rev/s

                                                 =  58 Hz

b) The Induced emf, ∈ = ωBπ$a^{2}$ /2

                 = $((364.4 rad/s)(15 × [tex]10^{-3}$ T)(π)(3.0 × $10^{-2}$ m)^2)÷2[/tex]

                = 0.007728 V

                =  7.73 mV