Part 3 problem solving write your complete solution

Part 3: Problem Solving
Write your complete solution and final answer.
1. A rectangular coil of N turns and of length a and width b is rotated at frequency f in a
uniform magnetic field B , as indicated in the figure . The coil is connected to co-rotating
cylinders, against which metal brushes slide to make contact. (a) Show that the emf
induced in the coil is given (as a function of time t) by
This is the principle of the commercial alternating-current generator. (b) Design a loop
that will produce an emf with E
0
= 150 V when rotated at 60.0 rev/s in a uniform
magnetic field of 0.500 T

2. A metal rod is forced to move with constant velocity along two parallel metal rails,
connected with a strip of metal at one end, as shown in the figure. A magnetic field B =
0.350 T points out of the page. (a) If the rails are separated by 25.0 cm and the speed of
the rod is 55.0 cm/s, what emf is generated? (b) If the rod has a resistance of 18.0 Ω and
the rails and connector have negligible resistance, what is the current in the rod? (c) At
what rate is energy being transferred to thermal energy?
3. A UHF television loop antenna has a diameter of 11 cm. The magnetic field of a TV
signal is normal to the plane of the loop and, at one instant of time, its magnitude is
changing at the rate 0.16 T/s. The magnetic field is uniform. What emf is induced in the
antenna?
4. The magnetic flux through the loop shown in Fig. 121P11-33 increases according to the
relation Φ B = 6.0t 2 + 7.0t, where Φ B is in milliwebers and t is in seconds. (a) What is
the magnitude of the emf induced in the loop when t = 2.0 s? (b) What is the direction of
the current through R?
5. What is the index of refraction in a medium where the speed of light is 1.5×10 8 m/s?
6. What is the speed of light in water whose refractive index is 1.33?
7. A ray of light is incident through glass, with refractive index 1.52, on an interface
separating glass and water with refractive index 1.32. What is the angle of refraction if
the angle of incidence of the ray in glass is 25 °?