Physics 2B Electricity and Magnetism. Instructor: Prof Benjamin Grinstein UCSD

Physics 2B Electricity and Magnetism Instructor: Prof Benjamin Grinstein UCSD

week 1

Rank in order, from most positive to most negative, the charges q a to q e of these five systems. 1. q a = q b > q e > q c > q d 2. q a > q e > q d > q c > q b 3. q e > q a > q d > q b > q c 4. q d > q c > q e > q a = q b 5. q d > q c > q e > q a > q b The charge of a system is the difference between the number of protons and electrons. For example, qa=1-0=1. A neutral glass ball has off equal number, say N, of electrons and protons. Removing 3 electrons gives qe=(n)-(n-3)=3

A plastic rod that has been charged to -15 nc touches a metal sphere. Afterwards the rod s charge is -10 nc. (a) What kind of charged particle was transferred between the rod and the sphere? Did it move from the rod to the sphere or in the opposite direction? (b)how many charged particles were transferred? Ans: (a) electrons have been added to the metal sphere (b) 3.1 x 10 10

Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges? 1) one is positive, the other is negative 2) both are positive 3) both are negative 4) both are positive or both are negative The fact that the balls repel each other only can tell you that they have the same charge, but you do not know the sign. So they can be either both positive or both negative. Follow-up: What does the picture look like if the two balls are oppositely charged? What about if both balls are neutral?

Two 1.0 g spheres are charged equally and placed 2.0 cm apart. When released they begin to accelerate at 150 m/s 2. What is the magnitude of the charge in each sphere? Ans: 82 nc

From the picture, what can you conclude about the charges? 1) have opposite charges 2) have the same charge 3) all have the same charge 4) one ball must be neutral (no charge)

From the picture, what can you conclude about the charges? 1) have opposite charges 2) have the same charge 3) all have the same charge 4) one ball must be neutral (no charge) The GREEN and PINK balls must have the same charge, since they repel each other. The YELLOW ball also repels the GREEN, so it must also have the same charge as the GREEN (and the PINK).

Electroscope (demo)

A metal ball hangs from the ceiling by an insulating thread. The ball is attracted to a positive-charged rod held near the ball. The charge of the ball must be: 1) positive 2) negative 3) neutral 4) positive or neutral 5) negative or neutral Clearly, the ball will be attracted if its charge is negative. However, even if the ball is neutral, the charges in the ball can be separated by induction (polarization), leading to a net attraction. remember the ball is a conductor! Follow-up: What happens if the metal ball is replaced by a plastic ball?

Answer: attraction, just like conductor

An electroscope is positively charged by touching it with a positive glass rod. The electroscope leaves spread apart and the glass rod is removed. Then a negatively charged plastic rod is brought close to the top of the electroscope, but it doesn t touch. What happens to the leaves? 1) The leaves get closer together. 2) The leaves spread further apart. 3) The leaves don t move. 4) One leaf moves higher, the other lower. Initially the positive charge spreads throughout the leaves and body of the electroscope. The nearing negative charge does not change the overall charge of the electroscope, but does change its distribution: the positive charge, being attracted towards the negatively charged plastic rod, moves from the leaves towards the body.

Two neutral conductors are connected by a wire and a charged rod is brought near, but does not touch. The wire is taken away, and then the charged rod is removed. What are the charges on the conductors? 1) 0 0 2) + 3) + 4) + + 5) While the conductors are connected, positive charge will flow from the blue to the green ball due to polarization. Once disconnected, the charges will remain on the separate conductors even when the rod is removed. 0 0 Follow-up: What will happen when the conductors are reconnected with a wire???

A 10.0-μC charge, q1, is at the origin. (a)find the force it exerts on a.5-μc charge, q2, at a point P with coordinates x=4.0 m, y=3.0m (b)find the electric field produced by the charge q1 at point P. (c)find the electric field produced by the charge q2 at the origin. 4 3 q 2 r y (m) 2 1 r 12 q 1 θ 0 1 2 3 4 5 x (m) Ans: (a) (1.44,1.08) mn, (b) (2.88, 2.16) kn/c, (c) (-0.144, -0.108) kn/c

(a) What is the net force on the charge at the origin? (b) What is the electric field at the origin? (c) What is the electric field at a point on the x-axis 4 m to the right of the origin? 3 + 3.2 µ C y (m) 2 1 4.6 µ C + 1 7.1 µ C 2 x (m) 3 Ans: (a) (73, 23) mn, (c) (-5.4, -0.69) kn/c

Interaction of Electric Charges (applet)

Charges A and B exert repulsive forces on each other. q A = 4q B. Which statement is true? 1) F A on B > F B on A 2) F A on B < F B on A 3) F A on B = F B on A

An electron is placed at the position marked by the dot. The force on the electron is 1) to the right. 2) to the left. 3) zero. 4) there is not enough information to tell.

You are sitting a certain distance from a point charge, and you measure an electric field of E 0. If the charge is doubled and your distance from the charge is also doubled, what is the electric field strength now? (1) 4 E 0 (2) 2 E 0 (3) E 0 (4) 1/2 E 0 (5) 1/4 E 0 Remember that the electric field is: E = kq/r 2. Doubling the charge puts a factor of 2 in the numerator, but doubling the distance puts a factor of 4 in the denominator, because it is distance squared!! Overall, that gives us a factor of 1/2. Follow-up: If your distance is doubled, what must you do to the charge to maintain the same E field at your new position?

Charge q2 is in static equilibrium. What is q1? Ans: 12.0 nc What is the force on the 1.0 nc charge (the one at the bottom)? Ans: 1.14 x 10-5 N up

Between the red and the blue charge, which of them experiences the greater electric field due to the green charge? 1) +1 2) +2 3) the same for both +1 +2 +1 +1 d d

Between the red and the blue charge, which of them experiences the greater electric field due to the green charge? 1) +1 2) +2 3) the same for both +1 +2 +1 +1 d d Both charges feel the same electric field due to the green charge because they are at the same point in space!

What is the electric field at the center of the square? -2 C 2 1 3 4 5) E = 0-2 C

What is the electric field at the center of the square? -2 C 2 1 3 4 5) E = 0-2 C For the upper charge, the E field vector at the center of the square points towards that charge. For the lower charge, the same thing is true. Then the vector sum of these two E field vectors points to the left. Follow-up: What if the lower charge was +2 C? What if both charges were +2 C?

What is the electric field at the center of the square? -2 C -2 C 2 1 3 4 5) E = 0-2 C -2 C

What is the electric field at the center of the square? -2 C -2 C 2 1 3 4 5) E = 0-2 C -2 C The four E field vectors all point outwards from the center of the square toward their respective charges. Because they are all equal, the net E field is zero at the center!! Follow-up: What if the upper two charges were +2 C? What if the right-hand charges were +2 C?

Two 5.0 g point charges on 1.0-m-long threads repel each other after being charged to +100 nc. What is the angle θ? (You can assume θ is small) Ans: 0.077 rad (that is, 4.4 deg)

Ans: 178 nc An electric field 100,000 N/C causes the 5.0 g point charge to hang at a 20 degree angle. What is the charge on the ball?