Physics 2BElectricity and

Magnetism

Instructor: Prof Benjamin GrinsteinUCSD

week 1

1. qa = qb > qe > qc > qd

2. qa > qe > qd > qc > qb

3. qe > qa > qd > qb > qc

4. qd > qc > qe > qa = qb

5. qd > qc > qe > qa > qb

Rank in order, from most positive to most negative, the charges qa to qe of these five

systems.

1. qa = qb > qe > qc > qd

2. qa > qe > qd > qc > qb

3. qe > qa > qd > qb > qc

4. qd > qc > qe > qa = qb

5. qd > qc > qe > qa > qb

Rank in order, from most positive to most negative, the charges qa to qe of these five

systems.

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 1010

1) one is positive, the other

is negative

2) both are positive

3) both are negative

4) both are positive or both

are negative

Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges?

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.

1) one is positive, the other

is negative

2) both are positive

3) both are negative

4) both are positive or both

are negative

Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges?

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/s2. What is the magnitude of the charge in each sphere?

Ans: 82 nC

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)

From the picture, what can you conclude about the charges?

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)

1) positive

2) negative

3) neutral

4) positive or neutral

5) negative or neutral

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:

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.

1) positive

2) negative

3) neutral

4) positive or neutral

5) negative or neutral

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:

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.

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) – –

0 0

? ?

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.

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) – –

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.

0 1

1

2

3

4

2 3 4 5q1

q2

r12

!

x (m)

y (m

)

r

Ans: (a) (1.44,1.08) mN, (b) (2.88, 2.16) kN/C, (c) (-0.144, -0.108) kN/C

1

2

3 +

+ –1 2 3

x (m)

y (m)

3.2 C µ

–4.6 C µ

7.1 C µ

(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?

Ans: (a) (73, −23) mN, (c) (-5.4, -0.69) kN/C

Interaction of Electric Charges

(applet)

1) FA on B > FB on A

2) FA on B < FB on A

3) FA on B = FB on A

Charges A and B exert repulsive forces on each other. qA = 4qB.

Which statement is true?

1) FA on B > FB on A

2) FA on B < FB on A

3) FA on B = FB on A

Charges A and B exert repulsive forces on each other. qA = 4qB.

Which statement is true?

1) to the right.

2) to the left.

3) zero.

4) there is not enough information to tell.

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.

An electron is placed at the position marked by the dot. The force on the electron is

(1) 4 E0

(2) 2 E0

(3) E0

(4) 1/2 E0

(5) 1/4 E0

You are sitting a certain distance from a point charge, and you measure an electric field of E0. If the charge is

doubled and your distance from the charge is also doubled, what is the electric field strength now?

Remember that the electric field is: E = kQ/r2.

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.

(1) 4 E0

(2) 2 E0

(3) E0

(4) 1/2 E0

(5) 1/4 E0

You are sitting a certain distance from a point charge, and you measure an electric field of E0. If the charge is

doubled and your distance from the charge is also doubled, what is the electric field strength now?

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

+2 +1+1 +1d d

1)

2)

3) the same for both

Between the red and the

blue charge, which of

them experiences the

greater electric field due

to the green charge?

+2

+1

Both charges feel the same electric

field due to the green charge because

they are at the same point in space!

+2 +1+1 +1d d

1)

2)

3) the same for both

Between the red and the

blue charge, which of

them experiences the

greater electric field due

to the green charge?

+1

+2

What is the electric field at

the center of the square?

43

2 1

-2 C

-2 C

5) E = 0

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.

What is the electric field at

the center of the square?

43

2 1

-2 C

-2 C

5) E = 0

Follow-up: What if the lower charge was +2 C? What if both charges were +2 C?

43

2 1

-2 C

-2 C -2 C

-2 C

What is the electric field at

the center of the square?

5) E = 0

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!!

43

2 1

-2 C

-2 C -2 C

-2 C

What is the electric field at

the center of the square?

5) E = 0

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 threadsrepel 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)

An electric field 100,000 N/C causes the 5.0 gpoint charge to hang at a 20 degree angle. What is the charge on the ball?

Ans: 178 nC