Electricity and Magnetism Study Questions

Bring on the tough stuff.

1. What is the difference between electric field ( E) and electric potential ( V)?

2. What is the electric field inside a hollow conducting sphere with charge q on its surface? What is the electric potential inside?

3. How much work does it take to push a charge around on an equipotential line in an electric field—say, in a circle around a second charge?

4. Which of the following two paths takes more work to push a charge along?

5. Should you hook up Christmas lights in series or parallel?

6. In an electric generator, such as a hydroelectric dam, mechanical energy is converted into electrical electricity. This is accomplished by using mechanical energy to turn a loop of wire in a constant magnetic field. Why does this create an emf?

7. In a speaker, an electromagnet is attached to the diaphragm (the round bouncy thing) and suspended above a permanent magnet. In order to make any given sound, the diaphragm must oscillate up and down at the frequency of the note it's creating—how can this configuration be used to accomplish that?

8. Why does Coulomb's Law make nuclear fusion difficult?

9. What are the differences between an inductor and a capacitor?

10. Explain Kirchhoff's two laws.

Answers

1. What is the difference between electric field ( E) and electric potential ( V)?

Electric field measures the force a +1 C charge would feel at that location; electric potential measures the work it would take to move a +1 C charge to that position. Field lines radiate out from charges, with an intensity falling off as ¹/_r². Potential falls off as ¹/_r, leaving equipotential lines—lines with the same associated electric potential energy—around the charge, which intersect field lines at right angles.

2. What is the electric field inside a hollow conducting sphere with charge q on its surface? What is the electric potential inside?

Inside a hollow sphere, the electric field is zero. This follows from Gauss' Law—with no charge inside the sphere, there can't possibly be an electric field. Another way to think about it is to visualize all the forces a charge at the center of the sphere would feel: with charge distributed evenly over the spherical shell, the center would feel equal forces in all directions. However, the potential in the middle of the sphere is not zero. It takes work to move a charge from infinity to the sphere. Once you push the charge through the surface of the sphere, you don't need to do any more work to move it around (there's no electric field), but it still took work to get to that point. The potential inside the sphere is the same at every point, and equal to the potential on the sphere's surface.

3. How much work does it take to push a charge around on an equipotential line in an electric field—say, in a circle around a second charge?

It take zero work to move a charge on an equipotential line. By definition, an equipotential line is a set of points where the electric potential is identical. That means every point on that line has exactly the same electric potential energy associated with it. With no change in energy, it takes no work to move from point to point.

4. Which of the following two paths takes more work to push a charge along?

It takes exactly the same amount of work to push a charge along either path. Electric potential energy is solely based on position, and is what we call path independent—it doesn't matter how you get from point to point, just where those points are. The net change in energy is always the same.

5. Should you hook up Christmas lights in series or parallel?

For the most part, parallel. In series, if one light goes out, the entire string will go out because there will no longer be any path for current to follow. But if the lights are hooked up in parallel, one light dying will not affect the rest, since current can still flow around the circuit.

6. In an electric generator, such as a hydroelectric dam, mechanical energy is converted into electrical electricity. This is accomplished by using mechanical energy to turn a loop of wire in a constant magnetic field. Why does this create an emf?

Faraday's Law states an emf is created any time there is a change of magnetic flux, which is defined as the number of field lines passing through an area A which is perpendicular to the field. As the wire rotates, the area that is perpendicular to the field is given by Acosθ, where θ is the number of degrees the wire has rotated through at that instant. This creates a constantly changing magnetic flux despite the constant area of the loop and constant strength of the magnetic field, and so an emf is born.

7. In a speaker, an electromagnet is attached to the diaphragm (the round bouncy thing) and suspended above a permanent magnet. In order to make any given sound, the diaphragm must oscillate up and down at the frequency of the note it's creating—how can this configuration be used to accomplish that?

As your tunes bump, an alternating electrical current is sent to the electromagnet, switching the direction current flows through the coil. This changes the polarity of the magnet, which is attracted-repulsed-attracted-etc. to the permanent magnet below it, moving the diaphragm and creating anything from Avicii bass drops to Vivaldi string concertos.

8. Why does Coulomb's Law make nuclear fusion difficult?

This is an effect known as the Coulomb barrier—it even popped up in The Avengers. As two nuclei get close enough to start to think about potentially deciding to maybe try to undergo fusion, the electrical repulsion between their protons, as described by the Coulomb force, becomes bigger and bigger. Scientists can push and push two protons together, but the fraction that have enough energy to break through the barrier is incredibly small. Quantum mechanics, in keeping with the superhero theme, comes to the rescue here eventually, but we're going to save that for the DVD.

9. What are the differences between an inductor and a capacitor?

An inductor stores energy in its magnetic field; a capacitor stores energy in its electric field. The energy stored in an inductor is based on the current flowing through it; the energy stored in a capacitor is based on the voltage across it. Inductors combine linearly in series; capacitors combine linearly in parallel. The symbol for an inductor looks like a squiggle; the symbol for a capacitor looks like a pair of parallel lines.

10. Explain Kirchhoff's two laws.

Kirchhoff's Current Law states that the net current flowing into a node of a circuit must equal the net current flowing out of that node. This is exactly analogous to water flowing in pipes—if you put three gallons of water in one pipe, three gallons of water better come out the other end; if you put three gallons of water through two pipes, you still better get three gallons at the end. Kirchhoff's Voltage Law states that the net voltage change around any loop in a circuit is zero. Any energy added to the circuit (for example, by a battery) will be stored or dissipated by another circuit element (resistors, capacitors, etc.).