1. If a bar magnet is broken into two pieces, how many magnetic poles are there?

2. A long straight wire carries a current in the direction shown in the following figure. At the point labeled A, is the direction of the magnetic field left, right, up. Down, into the page, or out of the page? What is the direction at point B? Explain.

3. Three long straight wires each carry identical current in the directions shown in the following figure. What is the direction of the net force on the wire at the right?

4. One of the Earth’s magnetic poles located in Antarctica. Is it a magnetic North Pole or magnetic South Pole?

5. Consider the case in which the north pole of a bar magnet is being moved away from a conducting cooper ring. Do the field lines created by the induced current point toward the bar magnet or away? Will this induced field pull back on the magnet or push it away? Explain.

6. In Chapter 10 we found that an infinite amount of energy is required to accelerate a massive particle to the speed of light. What does this imply about the mass of a photon?

7. Two students are discussing what happens when you turn down the rate at which electrons are fired at two slits. Tyson claims, “Because you still get an interference pattern even with only one electron at a time, each electron must interfere with itself. As weird as it sounds, each electron must be going through both slits.” Ulricht counters, “That’s crazy. I can’t be at class and on the ski slope at the same time. Each electron must pass through only one slit.” Which student is correct? Explain

8. In the two-slit experiment with photons, what type of pattern do you expect to obtain if you turn the light source down so low that only one photon is in the apparatus at a time?

9. Where would you most likely find the electron if it is in a quantum state with n = 3, L = 2, and M=-2 as shown in Figure 24-13?

10. Like light, electrons exhibit diffractions when passed through a single slit. Use the Heisenberg uncertainty principle to explain why narrowing the slit (that is, improving the knowledge of the electron’s position in a direction perpendicular to the beam) causes the diffraction pattern to get wider.

1. When a bar magnet is broken into two pieces, each piece becomes an individual magnet with two poles. Therefore, there would be four magnetic poles in total - two north poles and two south poles.

To get this answer, you can observe that when a bar magnet is broken, it does not eliminate the existence of the magnetic poles. Instead, each piece becomes a smaller magnet with its own set of poles.

2. To determine the direction of the magnetic field at point A in a long straight wire carrying current, you can use the right-hand rule. Point your right thumb in the direction of the current, and your fingers will curl in the direction of the magnetic field.

Based on the figure, if the current is flowing downward at point A, the magnetic field direction would be either into the page or away from the page - perpendicular to the direction of the wire.

For point B, you can follow the same right-hand rule as before. If the current is flowing from right to left at point B, the magnetic field would be either up or down, perpendicular to the direction of the wire.

3. To determine the direction of the net force on the wire at the right, you can use the right-hand rule again. Start by considering the magnetic field produced by the wire on the right. Wrap your right hand around the wire with your fingers pointing in the direction of the current. Your thumb will then point in the direction of the magnetic field produced by that wire.

Next, consider the interaction of the magnetic field produced by the wire on the right with the magnetic fields produced by the other two wires. The net force on the wire at the right will be in the direction of the resultant magnetic field formed by the interaction.

4. One of the Earth's magnetic poles located in Antarctica is a magnetic South Pole. This means it is the region of the Earth where the magnetic field lines point into the Earth's surface.

To determine this, you can refer to the convention that the side of a magnet that aligns with the Earth's magnetic South Pole is considered to be the magnetic North Pole, and vice versa.

5. When the north pole of a bar magnet is moved away from a conducting copper ring, the induced current in the ring creates a magnetic field. This induced field opposes the change in the original magnetic field.

So, the field lines created by the induced current will point in the opposite direction of the bar magnet's magnetic field, which is away from the bar magnet. This induced field will push the bar magnet, rather than pull it back, as it tries to counteract the change in the original magnetic field.

This behavior follows Lenz's Law, which states that the direction of an induced current will be such that it opposes the change that caused it.

6. The fact that an infinite amount of energy is required to accelerate a massive particle (with rest mass) to the speed of light implies that the mass of a photon must be zero.

This conclusion is based on Einstein's theory of relativity, which states that as an object with mass approaches the speed of light, its energy and momentum increase, requiring more and more energy to accelerate it further. Since a photon travels at the speed of light and has energy and momentum, but no rest mass, it must have zero mass.

7. Ulricht is correct. Each electron must pass through only one slit in the two-slit experiment.

When electrons are fired at the slits one at a time, they still produce an interference pattern. This phenomenon is known as the wave-particle duality of electrons (and all other particles). It means that electrons exhibit both wave-like and particle-like behavior.

Each electron behaves like a wave that can interfere with itself, resulting in an interference pattern on the screen behind the slits. However, once the electron is detected, it behaves like a particle and is found only at a specific location on the screen.

Tyson's statement about electrons interfering with themselves is a misunderstanding of the wave-particle duality concept. The interference pattern arises from the probabilistic nature of quantum mechanics, where the wave nature of particles leads to interference effects.

8. If you turn the light source down so low that only one photon is in the apparatus at a time in the two-slit experiment with photons, you would still expect to see an interference pattern.

Even with just one photon at a time, it will exhibit wave-like behavior and interfere with itself, resulting in an interference pattern over many trials.

This demonstrates the probabilistic nature of quantum mechanics, where each individual photon's behavior is uncertain, but their collective behavior, when observed many times, reveals the interference pattern.

9. In Figure 24-13, given that the quantum state of the electron is described as n = 3, L = 2, and M = -2, the most likely location to find the electron is in an orbital that satisfies these quantum numbers.

To determine the location, you can use the quantum numbers to identify the specific atomic orbital. In this case, n = 3 represents the principal quantum number, which specifies the energy level of the electron. L = 2 represents the azimuthal quantum number or orbital angular momentum quantum number, which determines the shape of the orbital.

M = -2 represents the magnetic quantum number, which determines the orientation of the orbital in space. Combining these quantum numbers, you can identify the orbital as a 3d orbital.

10. When electrons pass through a single slit, they exhibit diffraction, similar to light. The Heisenberg uncertainty principle provides an explanation for why narrowing the slit (improving the knowledge of the electron's position in a direction perpendicular to the beam) causes the diffraction pattern to get wider.

According to the Heisenberg uncertainty principle, there is a fundamental limit to the simultaneous knowledge of a particle's position and momentum. As the knowledge of the electron's position is improved (by narrowing the slit), the uncertainty in its momentum increases.

This increased momentum uncertainty means that the electrons will have a wider range of momenta after passing through the slit. Consequently, the spread in momentum leads to a wider diffraction pattern.

In other words, a more precisely defined position translates to a broader range of possible momenta, resulting in a wider diffraction pattern.