In many apartment buildings visitors must call the person they are visiting from the lobby to be "buzzed" in. The person in the apartment can push a button that will unlock the bolt on the front door of the building so that the visitor can enter. Consider the simple circuit and mechanical system shown below in the following problems.
1. When the switch is closed, current can flow through the wire of the electromagnet. When the current passes through the battery it obtains energy. When the current travels through the long wire forming the electromagnet it loses most of this energy. Compare the voltage at the point where current enters the electromagnet (point A) to the voltage where it leaves the electromagnet (point B).
Answer: The voltage at point A is higher than the voltage at point B.
Why: As a charge moves through the long wire some of its electrostatic potential energy is converted into thermal energy due to collisions with the atoms in the metal. Since voltage is a measure of the electrostatic potential energy of each charge, the voltage will decrease as the charges move through the wire.
2. When the switch is closed, compare the current (the number of electrons per second) entering the electromagnet at point A to the current leaving it at point B.
Answer: The current is the same at points A and B.
Why: Although the charges passing through the wire may bump into metal atoms, they are neither created or destroyed. The same number of charges must leave the wire each second as enter it, otherwise charge would accumulate endlessly as the circuit ran.
3. When the switch is open, is there a net charge on either side of the switch? If so, is it positive or negative? Be sure to answer for both sides of the switch.
Answer: Yes. The top of the switch is positively charged and the bottom is negatively charged.
Why: Since the positive charges at the top of the battery don't like to be near each other, they will spread out along the wire attached to the top of the battery. Positive charges will accumulate at the top of the switch. In a similar way, negative charges at the bottom of the battery will spread out through the wire attached to it.
4. When the switch is closed, the current flowing through the coil of wire will turn on the electromagnet. Assume that the bolt is a magnet with its north (labeled N) and south (labeled S) poles positioned as shown in the figure. Where should the north and south poles of the electromagnet be in order to attract the bolt toward the electromagnet and open the door?
Answer: The north pole should be on the left and the south pole should be on the right end of the electromagnet.
Why: Opposite poles attract with a force that increases as they get closer together. Like poles repel with a force that increases as they get closer. Although there is no net pole in either the bolt or the electromagnet, they will feel a net attractive force if they are arranged to have opposite pole close to each other.
5. With the battery positioned as shown in the figure, the bolt will open when the switch is closed. If the battery were put in backward, so that the positive terminal was on the bottom and the negative terminal on the top, would the bolt open when the switch was closed? Why?
Answer: No. The electromagnet would then have its south pole on the left and its north pole on the right resulting in a repulsive force (force to the left) on the bolt rather than an attractive one (force to the right).
Why: The poles of the electromagnet are reversed when the direction of the current through the coil is reversed.
6. If you move the electromagnet to the right, so that it is farther from the bolt, it may not be able to open the bolt when the switch is closed. Briefly explain why.
Answer: As the distance between the bolt and the electromagnet increases, the attractive force between them decreases.
Why: If the force provided by the electromagnet is less than the forces keeping the bolt in place (friction and the force of the spring) then the bolt will not open when the switch is closed.
7. If the electromagnet shown in the figure were not quite strong enough to open the bolt, you might consider adding a second battery to the circuit. To make the electromagnet stronger you need to increase the current through the coil. Increasing the voltage difference between its two ends (points A and B) will increase the current through the coil, making the electromagnet stronger. How would you add a second battery to increase the voltage difference across the coil?
Answer: Add the second battery in series with the first, with its negative end attached to the positive end of the first battery.
Why: When a charge passes through this pair of batteries it will gain twice as much electrostatic potential energy, which can then be released in the coil.
8. Adding lots of batteries in the proper way would make both the voltage drop across the coil and the current through the coil large when the switch is closed. Although this would make the automatic lock very reliable since the electromagnet would be very strong, it may also be a fire hazard. Briefly explain why by describing where most of the energy is deposited in the circuit and what form that energy takes.
Answer/Why: As the current travels through the battery it gains energy. In the long coil of wire forming the electromagnet, most of this electrostatic potential energy is wasted as thermal energy. If the voltage and current through the wire are both large then the amount of power being consumed will also be very large and thermal energy will be deposited in the wire very quickly.