212 - Problem Set 7

Physics 212 Spring 2009 Problem Set #7

1)A

uniform magnetic field of magnitude 0.078 T passes through a circular area of radius 0.1 m. The magnetic field lines are oriented at an angle of 25° with respect to a line that is normal to the circular area. Calculate the flux through the surface.

2)Skid is flying his Cessna Citation II twin engine jet.

The length of the wings from tip to tip is 59 m. The jet is flying horizontally at a speed of 220 m/s. The earth’s magnetic field has a vertical component of magnitude 5.0 x 10-6 T. Calculate the induced EMF between the wing tips.

3)

A straight wire is partially bent into the shape of a circle as shown below. The radius of the circle 2.0 cm. A uniform magnetic field of magnitude 0.55 T is directed perpendicular to the plane of the circle. Each end of the wire is then pulled so that the area of the circle shrinks to zero. This is done during a time of 0.25 s. Calculate the magnitude of the average induced EMF between the ends of the wire.

4)

A circular loop of wire with a radius of 20 cm is placed in a uniform magnetic field of 0.2 T. The field is perpendicular to the plane of the loop. The loop is removed from the field in 0.3 s. Calculate the average induced EMF in the loop while it is being pulled out of the field.

5)

A long, straight wire has a current running through it. Above the straight wire is a loop of wire that is moved towards the straight wire. The loop then passes over the straight wire and continues downward, away from the straight wire. See diagram. Determine the direction (clockwise or counterclockwise) of the induced current in the loop as it is (a) moved towards the wire from above, (b) moved away from the wire.

7)Skid needs to design a 60 Hz AC generator to run his stage amplifier for his gig at Lollapalooza. The generator needs to contain a 150-turn coil whose area per turn is 0.85 m2 while its maximum EMF needs to be 5500 V. What should be the magnitude of the magnetic field in which the coil rotates? 8)

A 300-turn solenoid has a radius of 5 cm and a length of 20 cm. Find the energy stored in it when the current is 0.5 A.

9)

A step-up transformer is designed to have an output voltage of 2200 V (rms) when the primary is connected across a 110 V (rms) source. (a) If there are 80 turns on the primary winding, how many turns are required on the secondary? (b) If a load resistor across the secondary draws a current of 1.5 A, what is the current in the primary, assuming ideal conditions?

ANSWERS: 1) 2.2 mWb 2) 65 mV 3) 2.8 mV 4) 84 mV 7) 0.11 T

8)5.55 x 10 9)

6)

Find the direction of the induced current through the resistor in the drawing below (a) at the instant the switch is closed, (b) after the switch has been closed for several minutes, and (c) at the instant the switch is opened.

J a) 1600 turns b) 30 A -4