Some additional concept questions to help you review:
- I have three metal balls, A, B, and C. One or more of these objects may be charged. I observe that A and B attract each other, and B and C attract each other. Can objects A and C both be neutral? Can they both be positive? Can they be oppositely charged? Explain your answers to these three questions.
Attraction can be either due to induced charges or due to the net charges of the objects. So for example, A and B could be oppositely charged to cause their attraction, or only one of them could be charged and the other one is attracted by induced charges. Answers: A and C can both be neutral; if B is charged then it would attract them both by induction. A and C could both be positive; if B is neutral then it would attract them both by induction. A and C could be oppositely charged; if B is neutral then again it would attract them both by induction.
- In class, I demonstrated a device called the Windhurst generator (although I didn’t mention its name that day). It was the demonstration that I turned a crank by hand which then generated a spark between two metal balls. The spark had a certain amount of charge transferred, a certain voltage between the two metal balls, and a certain electric field between the metal balls. How do these three quantities (Q, V, E) compare with that of a lightning bolt – that is, obviously the lightning bolt is bigger in some respects, but which respects? Is the lightning bolt the roughly same in any of these quantities?
Sparks and lightning occur when you get dielectric breakdown of air, which happens at a particular electric field strength as discussed in class. So E is the same for sparks and for lightning. Q and V are much bigger for the lightning bolt.
- An electron starts at rest in an electric field, and then moves from x=0 m to x=1 m (to the right). What is the direction of the electric field? Where is the electric potential higher, at x=0 m or x=1 m?
Electrons feel a force in the opposite direction of E. Thus, the E field points to the left (negative x direction) since the electron moves to the right. Likewise, the convention for electrons is that they like to move from low potential to high potential, so the electric potential must be higher at x=1 m.
- A small coin with a charge of Q = -2 mC starts with velocity v=1 cm/s at point A, where the potential is 7 V. It moves for a while and then we observe it’s at point B, where the potential is 5V. Has the coin sped up or slowed down by the time it’s at point B? What if it’s original velocity is not in the same direction as the electric field, does that change your answer?
The coin moves from high potential to low potential. However, it would “like” to move from low to high, since it is negatively charged. That means it takes energy to move to the lower potential, that is, its kinetic energy gets converted into EPE. So, the coin slows down as it moves to point B, keeping EPE+KE constant. This does not depend on the direction of the velocity; the only thing that matters is that EPE+KE = total Energy, and as the coin moves to lower potential EPE increases and KE decreases.
- Suppose we want to place four charges onto the corners of a long, skinny rectangle. Two of the four charges are +1 mC, the other two are –1 mC. Where should the four charges be placed to maximize the stored electrical potential energy, using the usual convention that two charges infinitely far apart have zero EPE.
EPE = k q1 q2 / r. If we place the two + charges nearby each other, you get a big EPE as the formula gives a postive number for the product q1 q2, divided by a small number (their separation). Likewise for two – charges nearby each other. Then there is an additional contribution from having a + and – charge far away (along the long edge of the rectangle). This contribution to the EPE is negative (the product q1 q2 is negative) but it’s smaller as ‘r’ is a much bigger number. Note also that you have to add in the EPE for the particles that are diagonally opposite, but again it’s small for the same reason (‘r’ is big). So in total for four charges you have to use the EPE equation 6 times, but the biggest contribution to the EPE comes from the two pairs of charges close together, and to make EPE maximum you want these two pairs of charges to be pairs of like-sign charges.
- I have a cubical box, 1x1x1 meter. I place this box in a uniform electrical field E=45 N/C pointing to the left. What is the net electrical flux coming through this box, and is it into the box or out of the box?
From Gauss’s law, total flux = charge enclosed / epsilon0. No charge is enclosed, so the total flux = 0. Another way to say it is, the field lines entering the box due to the field all leave the box on the other side, so the net number of field lines entering is zero.
- I have a cubical box, 1x1x1 meter. Inside this box I place a +1 C charge. Is the net electrical flux through the box zero or not? If not, is it going into or out of the box? Does the answer change if it’s a –1 C charge?
Now the flux is not zero, again by Gauss’s Law. Since the charge is + field lines point away from it, so they exit the box – thus the flux is going out of the box. If the box had a –1 C charge the flux would be coming into the box.
- What’s the difference between an insulator and a conductor? If we had an object, what sort of tests could we do to determine which one it is?
Charges can freely move around inside conductors, but they don’t move easily inside an insulator. There’s lots of tests we could do. For example, hook it up to a battery and measure the current with an ammeter, conductors have low resistance (thus high current by Ohm’s Law) and insulators have high resistance (low current). Or, charge up one side of the object and then see if the other side is charged – an insulating rod for example would not have the far end of the rod charged, but a conductor would result in a charge all over.
- I have three objects that are all charged, and each of them repels the other two. Is this possible? If so, what are the signs of the charges on the objects?
Yes, if all the charges have the same sign then they all repel.
- I have three objects that are all charged, and each of them attracts the other two. Is this possible? If so, what are the signs of the charges on the objects?
No, this is impossible. Opposite charges attract, so the first object can be + and the second -, but then the third cannot be oppositely charged of the original two.