Physics 101 Homework Set 11 Solutions Exercises: ---------- Chap 24: -------- 2: Not all iron materials are magnets. For a piece of iron to be a magnet, most of the individual iron atoms need to be oriented in the same direction. In non-magnetized iron, the individual iron atoms are pointing in random directions so their magnetic fields cancel out. 8: The force of the electric field on the electron does not depend on the speed of the electron. The force of the magnetic field on the electron is zero if the electron is not moving. There is only a magnetic force on the electron if the electron is moving. 18: Food cans are made from iron (or steel which is 90+% iron) coated with tin or zinc. If a piece of iron is in a magnetic field, the magnetic field makes the magnetic domains line up temporarily. The longer the iron is in the magnetic field, the more domains permanently change their orientation to line up with the magnetic field. You can magnetize an iron bar by either a) placing it in a very strong magnetic field for a short time or b) placing it in a weaker magnetic field for a longer time. A can of food in your pantry is likely to be in the same position for months. Thus, it is exposed to the Earth's weak magnetic field in exactly the same orientation for months. This magnetizes it slightly. You can check this with some iron filings to see if they are attracted to the can. 20: The compass aligns itself with the magnetic field lines. The magnetic field lines point toward the North Pole. This does not change when you go south of the equator. Figure 24.19 shows a picture of the magnetic field lines around the Earth. (Note that if you bring a compass to the North Pole, it will try to point down. This is why compasses are useless near the magnetic north pole.) 22: 50 N. Newton's 3rd Law. 28: Magnetic fields make particles go in circles. They do not make particles go faster (since the force is always perpendicular to the velocity). Electric fields are needed to make the particles go faster. 30: If two particles are deflected in opposite directions (ie: one bends upward and one bends downward), then they must have opposite charge. (They have the same velocity and experience the same magnetic field, therefore the only thing that can be different is their charge.) 34: Northern Canada is closer to North Pole than Mexico. Cosmic rays moving toward the Earth above Mexico experience a magnetic field perpendicular to their velocity and are deflected. Cosmic rays moving toward the Earth above Northern Canada experience a magnetic field mostly parallel to their velocity and are not deflected much. (An alternate explanation is that cosmis rays tend to spiral around the magnetic field lines. Since the magnetic field lines hit the Earth near the poles, there will be much more cosmic ray intensity there.) Chapter 25: ----------- 2: Because iron amplifies the magnetic fields. Therefore, the magnitude of the changing magnetic fields will be larger, increasing the effects of induction. 4: When you turn the generator, you are supplying the energy needed to a) overcome friction and b) power the devices attached to the circuit. This means that when the generator is attached to circuit, you have to do work (W = F times d) to provide the energy used by the light bulbs or whatever is attached to the circuit. 10: An earthquake will shake (ie: move) the box. Since the magnet is suspended inside the box, there will be no force on the magnet and it will not move (principle of inertia). Therefore the coils inside the box will move with respect to the magnet and generate a voltage by induction. 18: Moving the magnet through the loop induces a voltage. The current caused by the voltage is I = V/R. When there are two loops of wire, there is twice the voltage. However, the resistance will also be double since the wire is twice as long. If you double both V and R, then I will not change. 26: There are two transformers here. The first is a 100:10 transformer and the second is a 10:100 transformer. Therefore, the second will reverse the effects of the first so that the output voltage of the second transformer equals the input voltage of the first transformer = 120 V. Now let's solve this in all its detail. First we solve for the voltage at the output of the 1st transformer. 120 V x ----- = ----- 100 t 10 t so x = 12 V. The output of the first transformer is the input to the second transformer. Now we have 12 V and 1 A at the input to the second transformer. We will solve for the output of the second transformer. 12 V y ---- = ---- 10 t 100 t so y = 120 V. That's what we got from the argument in the first paragraph (whew!). Now we use (IV)primary = (IV)secondary or 1 A * 12 V = z * 120 V so that z = 0.1 A. Thus, there are 120 V across and 0.1 A through the light bulb. 27: Zero. Zip. None. Nada. The input is DC. This means that the current is not changing, therefore the magnetic field is not changing, therefore there is zero induced voltage. 34: The problem with this scheme is that transformers can only change the voltage and current (amperage), they cannot change the power. Since energy is conserved, this means that all of the power output of the generator is needed to run the motor and all of the power output of the motor is needed to run the generator. There is no extra power to run light bulbs or other devices. In practice, even without taking electricity for other uses, friction will make the system run slower and slower. Note that this is a specific example of a 'perpetual motion machine'. Machines cannot generate power without an energy source, either fuel or sunlight or wind power or ... Lots of inventors keep trying to invent machines that can provide power without an energy source. The US Patent Office will not even look at these ideas since they violate the law of conservation of energy. Unfortunately, lots of people are suckered into investing in these schemes. --------------------------------------------------------- Problems: --------- Chap 25: -------- 2: a) To find the voltage across the secondary we have: 12 V x ---- = ----- 50 t 250 t so that x = 60 V. b) 60 V across 10 Ohms gives a current of 6 A (using V = IR) c) The power supplied to the primary must equal the power used by the secondary. The power used by the secondary is P = IV = 6 A * 60 V = 360 W. ------------------------------------------------------------- Estimation: ----------- Estimation 11: Your computer's disk drive holds 100 GigaBytes of data (that's 10^11 Bytes = 8*10^11 bits). The bits are encoded on the disk drive by small regions that are magnetized in one direction or another (eg: either up or down). How large a region does it take to encode one bit of data? Express your answer in square meters (m^2). If each region is a square, how long is the side of the square? (If the square is 9 m^2 then the side of the square is 3 m. If the square is 0.01 m^2 then the side of the square is 0.1 m.) Answer: My hard drive is about 10 cm across, which is 0.1 m. Therefore its area is about 0.1 m * 0.1 m = 0.01 m^2. (I don't care about the numerical difference between a 10 cm square and a 10 cm circle. It's about 25% which is less than all the other approximations that I will make.) This 0.01 m^2 holds approximately 10^12 bits. Thus, 10^12 bits use an area A = 0.01 m^2 so 1 bit uses an area A = 0.01 m^2 / 10^12 = 10^(-14) m^2. Wow, that's tiny! By comarison, a red blood cell is about 5*10^(-6) m across and has an area of about 3*10^(-11) m^2. This is 3000 times smaller than the area of a blood cell! The area would by A = 10^(-14) m^2 = [10^(-7) m]^2 so that it would be a square 10^(-7) m on a side.