Problem (1)a) State in words Faradays Law of Induction. b) A uniform magnetic field B is perpendicular to a circular loop of wire of 100-turns and negligible resistance, as shown in Figure (P-1-b). The field changes with time as shown (the z direction is out of the page). The loop is of radius r = 50 cm and is connected in series with a resistor of resistance R = 20 . The "+" direction around the circuit is indicated in the figure.

Fig. (P-1-b)a) What is the expression for EMF in this circuit in terms of Bz(t) for this arrangement? b) Plot the EMF in the circuit as a function of time. Label the axes quantitatively (numbers and units). Watch the signs. Note that we have labeled the positive direction of the emf in the left sketch consistent with the assumption that positive B is out of the paper. c) Plot the current I through the resistor R. Label the axes quantitatively (numbers and units). Indicate with arrows on the sketch the direction of the current through R during each time interval. d) Plot the rate of thermal energy production in the resistor.

Problem (2)a) How does Faraday's Law of electromagnetic induction relate to the voltage output of a DC generator? According to Faraday's Law, what factors can we alter to increase the voltage output by a DC generator? b) Figure (P-2-b) shows an AC generator. The generator consists of a rectangular loop of dimensions a and b with N turns connected to slip rings. The loop rotates with an angular velocity in a uniform magnetic field B.

Fig. (P-2-b)

1) Show that the potential difference between the 2 slip rings is = NBab sin t. 2) If a = 1 cm, b = 2 cm, N = 1000 and B = 2 T, at what angular frequency must the coil rotate to generate an emf whose maximum value is 110 V?3) Find the magnitude and direction of the net force exerted by the magnetic field if the loop is supplied with a current I = 2 mA in a clockwise direction. 4) Find the magnitude and direction of the net Torque exerted by the magnetic field on the loop.

Problem (3)a) State in words Lenzs Law of Induction. b) A circular wire loop sits inside a larger circular loop that is connected to a battery as shown in Fig. (P-3-b). Determine the direction of the convention current induced in the inner loop when the switch in the outer circuit is closed.

Fig. (P-3-b)

c) A central loop of wire lies inside a larger loop, which is connected to a battery as shown in Fig. (P-3-c). Current flows around this outer loop. The resistance of the outer loop is increasing. Determine the direction of the conventional current induced in the inner loop using Lenz Law.Fig. (P-3-c)

Problem (4) State in words Lenzs Law of Induction. Explain how to apply Lenzs Law for the following cases:Lenz's law states: . a) As the strong bar magnet approaches the suspended aluminum ring, a current is induced and the ring is repelled. Explain why. What happens when the magnet is taken away from the ring?

b) A circular wire loop is falling toward a standing magnet as shown here. Determine the direction of the conventional current induced in the loop as the loop approaches the magnet.

c) The conducting rectangular loop enters the magnetic field shown. What is the direction of the conventional current induced in the loop as it enters the field?

d) The conducting rectangular loop falls through the magnetic field shown. What is the direction of the conventional current induced in the loop as it leaves the field?

Problem (5)a) In an AC generator, a coil enclosing an area A and containing N turns, rotating with constant angular speed in a magnetic field. Prove that the emf induced in the loop varies sinusoidally in time.

b) Explain what will happen to the emf generated in the coil ifi. replacing the coil wire with one of lower resistanceii. spinning the coil faster iii. increasing the magnetic field iv. Increasing the number of turns of wire on the coil.c) An AC generator consists of 8 turns of wire, each of area A = 0.09 m2, and the total resistance of the wire is 12.0 . The loop rotates in a 0.500-T magnetic field at a constant frequency of 60.0 Hz.i. Find the maximum induced emf.ii. What is the maximum induced current when the output terminals are connected to a low-resistance conductor?

Problem (6)Figure (P-2) shows a zero-resistance rod sliding to the right on two zero-resistance rails separated by the distance L = 0.45 m. The rails are connected by a 12.5 resistor, and the entire system is in a uniform magnetic field with a magnitude of 0.75 T. (a) If the velocity of the bar is 5.0 m/s to the right, what is the current in the circuit? (b) What is the direction of the current in the circuit? (c) What is the magnetic force on the bar? (d) What force must be applied to keep the bar moving at constant velocity?

Figure (P-2)

Problem (7)If the magnetic field in a region varies with time according to the graph shown in Figure (P-3), find the magnitude of the induced EMF in a single loop of wire during the following time intervals: (a) 0-2.0 ms, (b) 2.0-4.0 ms, and (c) 4.0-8.0 ms. The loop has area 0.500 m2 and the plane of the loop is perpendicular to the B-field.

Figure (P-3)

Problem (8)Figure (P-6) shows a coil consisting of 100 turns, each carrying 3A of current and having an area 0.2 m2, is oriented such that its normal makes an angle of 90 with a B-field of 0.5T. a) Find the total torque on the coil. b) Whats the direction of rotation?

Figure (P-6)

Question (9)A long straight wire carries a current of 20 A, as shown in the figure (P-1). A rectangular coil with 2 sides parallel to the straight wire has sides 5 cm and 10 cm with the near side at a distance 2 cm from the wire. The coil carries a current of 5 A. (a) Find the force on each segment of the rectangular coil due to the current in the long straight wire. (b) What is the net force on the coil?(Hint: the magnetic flux produced by a conductor carrying current I is B=oI/2r)

Figure (P-1)Question (10)The following graph (P-10) is plotted for a magnetic flux crossing a single loop as function of the time, (t). Using Faradays law, plot the induced emf as a function of time on the provided grid below:

Figure (P-10)Problem (11)A 100-loop square coil of wire, with side l = 5.00 cm & total resistance 100 , is positioned perpendicular to a uniform 0.600-T magnetic field. It is quickly pulled from the field at constant speed (moving perpendicular to B) to a region where B drops to zero. At t = 0, the right edge of the coil is at the edge of the field. It takes 0.100 s for the whole coil to reach the field-free region. Find: (a) The rate of change in flux through the coil, and (b) The emf and current induced.(c) The energy dissipated in the coil. (d) The average force required (Fext).

Problem (12)a. State in words Faradays Law of Induction. b. Figure is a graph of the induced emf versus time for a coil of N turns rotating with angular speed in a uniform magnetic field directed perpendicular to the axis of rotation of the coil. What If ? Copy this sketch (on a larger scale), and on the same set of axes show the graph of emf versus t (a) if the number of turns in the coil is doubled; (b) if instead the angular speed is doubled; and (c) if the angular speed is doubled while the number of turns in the coil is halved.

Problem (13)a. State in words Lenzs Law of Induction. b. A conducting rod of length l = 35.0 cm is free to slide on two parallel conducting bars as shown in Figure. Two resistors R1 = 2.00 and R2 = 5.00 are connected across the ends of the bars to form a loop. A constant magnetic field B = 2.50 T is directed perpendicularly into the page. An external agent pulls the rod to the left with a constant speed of v = 8.00 m/s. Find (a) the currents in both resistors, (b) the total power delivered to the resistance of the circuit, and (c) the magnitude of the applied force that is needed to move the rod with this constant velocity.

Problem (14)a. What is the magnetic flux?b. The rotating loop in an AC generator is a square 10.0 cm on a side. It is rotated at 60.0 Hz in a uniform field of 0.800 T. Calculate (a) the flux through the loop as a function of time, (b) the emf induced in the loop, (c) the current induced in the loop for a loop resistance of 1.00 , (d) the power delivered to the loop, and (e) The torque that must be exerted to rotate the loop.