Homework 11 Solutions Physics 101 Lawrence Weinstein Exercises: ------------------------------ 24.4: When you strike the nail, you are shaking up the magnetic domains. The Earth's magnetic field exerts a torque on them and makes them tend to realign themselves with the direction of the Earth's field. By aligning the magnetic domains, it makes the nail a (relatively weak) magnet. 24.8: A stationary electric charge is surrounded by an electric field. When it moves, it is surrounded by both an electric and a magnetic field. 24.16: A dip needle or compass needle will swivel to point parallel to the magnetic field lines. The field lines are parallel to the Earth's surface at the equator and they point almost vertically at the poles. Therefore, a dip needle will point most nearly vertically at the poles and it will point horizontally at the equator. See figure 24.20 for a diagram of the Earth's magenetic field. (Note that this is a cutaway picture of the Earth. The closely spaced lines in the middle of the figure are going through the center of the Earth, not the outside.) 24.24: 50 N. Newton's 3rd Law. 24.32: If the beam of electrons is not deflected, then the magnetic field is parallel to its velocity. (When the magnetic field is parallel to the velocity, then the magnetic force is zero.) 24.34: If the magnetic field becomes stronger, then the magnetic force on the proton increases. The larger the force, the smaller the circle the proton will travel around (and the smaller the diameter of its circular path). There are two explanations for this: 1) In the absence of force, the proton will travel in a straight line. A small force would make the proton's path curve gently and go around a large circle. A large force will make the proton's path curve abruptly and go around a small circle. 2) To make a particle go in a circle, you need to apply a centripetal force F = mv^2/r. Since neither the mass nor the speed of the particle changes, if F increases, then the radius of the circle r must decrease. 24.36: The magnetic force changes the direction (see 24.34) of the particle but not its speed. The magnetic force is always perpendicular to the velocity of the particle. Therefore, the force does not do any work. Work (see chapter 6) equals the force times the component of the distance in the direction of the force. Since the force is always perpendicular to the velocity, the component of the distance in the direction of the force is zero. Magnetic forces do no work and therefore cannot change the kinetic energy. Note that this is similar to the case of the effects of gravity on circular orbits. Gravity always pulls radially and the moon (or other satellite) is always moving tangentially. Gravity does no work and the kinetic energy of the satellite does not change. 25.2: If the guitar has nylon strings, then the small permanent magnet will not magnetize the strings. This means that the strings will NOT induce a voltage in the coil. 25.12: The massive magnet is suspended inside the box by a long thin string (think of it as a pendulum hanging from the top of the box). When the earthquake makes the box move, it does not make the massive magnet move (not to begin with). This is due to the principle of inertia. Since the earthquake does not exert a force on the magnet, the magnet does not move. The box (and the coil) moves with respect to the magnet. Since the coil moves with respect to the magnet, the magnet induces a current in the coil. (Note that, since the box moves, the attachment point of the string moves, and therefore the pendulum will eventually move a bit.) 25.16: A generator moves a magnet with respect to a coil of wire. When the generator is spinning faster, the magnet is moving faster with respect to the coil. Therefore, the magnetic field is changing faster, therefore the induced voltage is greater. 25.18: This is the same situation as the ring shooter. The rapidly changing magnetic field induces an electric potential around the ring. The electric potential (voltage) makes a current flow around the ring. Power = current * voltage so that a lot of electric power is induced in the ring and turned into heat by the resistance. 25.24: We did this in class. Closing the switch makes a current flow in the primary coil. This makes a magnetic field that extends into the secondary coil. This changing magnetic field induces a voltage in the secondary coil. If you place an iron core in the coils, then the iron will amplify the magnetic field seen by the secondary coil. The larger changing magnetic field seen by the secondary coil will induce a larger voltage in the secondary coil. (Note that the voltage in the primary coil will not change. That is supplied by the battery.) 25.26: The power supplied to the primary coil of a transformer equals the power out of the secondary coil. P_p * I_p = P_s * I_s. If the secondary voltage is twice the primary voltage, then the secondary current must be half the primary current. 25.34: Zero. The voltage and current supplied to the primary coil are DC. 25.44: We know that energy is conserved, therefore this scheme cannot work. Now we have to figure out what is wrong with it. The problem refers to 'electricity that is stepped up with transformers'. This is not defined. 'Electricity' refers to a large range of phenomena and has many characteristics (eg: current, voltage, power). Transformers can 'step up' voltage (if they decrease current) or they can 'step up' current (if they decrease voltage) but they cannot change the power. Problems: ------------------------- 25.2: a) V_p / 50 turns = V_s / 250 turns V_s = 250 turns * (V_p / 50 turns) V_s = 250 turns * (12 V / 50 turns) V_s = 60 V b) This is just a simple curcuit problem: I_s = V_s / R = 60 V / 10 Ohms = 6 A c) Power is conserved in an ideal transformer Power supplied to primary = power out of secondary P_p = P_s = I_s * V_s P_p = 6 A * 60 V = 360 W Estimation: -------------------------- If a hard drive contains 100 GB of data, how much space does 1 bit take up? A hard drive is about 4" square or about 10 cm by 10 cm. Therefore, the area of a hard drive is (0.1 m)^2 = 0.01 m^2 = 10^(-2) m^2. Each 10^(-2) m^2 contains 8*10^11 bits (for a 100 GB drive). Therefore there are 10^(-2) m^2/drive ------------------- = 10^(-14) m^2/bit 8*10^11 bits/drive That is VERY small. This is a square with side = sqrt(10^(-14) m^2) = 10^(-7) m. This is tiny. By contrast, a human hair is 2-3*10^(-5) m in diameter, or about 250 times thicker. Wow!