AP Physics 2 – Magnetism Review Questions

1. A kid living in Montana USA owns a beanie that has a propeller on top.  He notices that every time he sets the beanie on the table the metallic propeller rotates so that it aligns north and south.  The propeller of his beanie is magnetic!  (a) The side of the propeller that turns toward Canada is which pole?  (b) Suppose he is wearing the beanie and facing toward Mexico – the magnetic field generated by the propeller points in what direction in the vicinity of his ears?  (c) If he wants the propeller to reverse direction  (while still facing Mexico) he should hold up a bar magnet with which pole near the propeller?

2. A thin flexible plastic refrigerator magnet is a material manufactured to have individualized magnetic parts a few millimeters in size in a pattern shown by the cross sectional diagram below.  Each arrow represents the dipole field of that section of the material.  The result of this structure is that the magnet will stick to the refrigerator only on one side.  (a) Sketch the magnetic field in and around the magnet (cross section view).  Label each triangle with north and south poles.  (b) Which side sticks to the refrigerator?  Why?  (c) Can one of these type magnets attract or repel another of these types?  Discuss.

3. The magnetic field of a cylindrical solenoid is given by the formula B = μ₀NI/L and it is relatively uniform throughout the volume.  Suppose a certain solenoid is a cylinder of length 30.0 cm and diameter 5.00 cm with 760 turns.  If placed in a vacuum a charged particle could either move in a circular path inside the solenoid or spiral through the cylinder from one end to the other.  (a) If a current of 8.00 A is used what, is the greatest speed proton that could be contained in the solenoid?  (b) With the same current, an electron with speed 6.0 ×10⁶ m/s would have a path with what radius and circle in what direction relative to the current?  (c) Challenge problem:  A proton with speed 85 km/s follows a helical path with radius 2.0 cm from one end of the cylinder to the other, spiraling with a frequency of 650 kHz.  Determine the current in the solenoid that would make this possible and the number of spirals completed as it passes through.  Hint: consider two components of velocity – one parallel to field and one perpendicular to field.

4. A current of 7.00 A flows down a long straight wire.  At the end of the wire there is a connection to two long straight wires, parallel to the first, that carry current back to the power source.  A cross section of the wires shown below shows that each wire is equidistant from the other two wires – forming an equilateral triangle 3.00 mm on each side.  Find the magnetic field at the center of each side of this triangle.  Ignore earth’s field.

5. Suppose the wires in the previous problem are 3.00 m long – determine the net force that acts on each wire.

6. A circular coil of wire with radius 2.0 cm, 45 turns, and resistance 5.0 ohms is placed flat on a table top and connected to an ammeter with resistance 80.0 ohms.  A bar magnet is held vertically with one end touching the table in the center of the coil.  The bar magnet is quickly removed upward and away from the coil in 0.20 seconds.  The ammeter indicates a clockwise current of 60.0 μA as the magnet is removed.  (a) Determine the emf induced in the coil.  (b) Estimate the strength of the bar magnet’s field near the poles.  (c) Which pole of the bar magnet was resting on the table?  Explain.

7. Sorry this is a short set of problems!  Try working examples from the Giancoli book or the Open Stack online book!

Answers:

1. a. The side toward Canada is the north pole of the magnetic propeller.
b. If facing Mexico, the magnetic field of the propeller points south in the vicinity of his ears.
c. Holding up a bar magnet with its south pole nearest the propeller tend to make it rotate.

2. a. Sketch of field should show loops that follow the arrows and stick out on the top side.
b. The top side of the diagram is the side that would stick.  The magnetic fields sticking out on that side would induce dipoles in the steel of the refrigerator door and cause an attraction.  Because the field does not stick out much on the bottom side it would have little effect.
c. Another magnet like this could conceivably attract or repel, but the fields would have to line up just right – if the magnetic regions are not precisely the same size this would be impossible.

3. a. 61.1 km/s
b. 1.3 mm, circulating in the same direction as conventional current in the solenoid
c. 13 A, 8.3 loops

4. Bottom side 0.539 mT, 180.0°; left side 1.43 mT, 139.1°; right side 1.43 mT, 199.1°

5. Each bottom wire 4.24 mN down, top wire 8.49 mN up

6. a. 5.1 mV
b. 18 mT
c. The north pole was down on the table so that there was originally a downward field inside the coil.  When the magnet is removed the downward flux is decreasing.  By Lenz’s law the induced current creates a field that also points down in order to oppose the change in flux.  In order to produce a downward field the conventional current in the coil must flow clockwise by the right hand rule.