one is positive, the other is negative one is positive, the other is negative both are positive both are positive both are negative both are negative both are positive or both are negative 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?

A) have opposite charges B) have the same charge C) all have the same charge D) one ball must be neutral (no charge) From the picture, what can you conclude about the charges?

A) positive B) negative C) positive or neutral D) 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:

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? A)00 B)+– C)–+ D)– – 0 0 ? ?

A B C D E F Two uniformly charged spheres are firmly fastened to and electrically insulated from frictionless pucks on an air table. The charge on sphere 2 is three times the charge on sphere 1. Which force diagram correctly shows the magnitude and direction of the electrostatic forces?

A) 3/4 N B) 3.0 N C) 12 N D) 16 N If we increase one charge to 4Q, what is the magnitude of F 1 ? 4Q Q F 1 = ? F 2 = ? Q Q F 1 = 3N F 2 = ?

A) 9 F B) 3 F C) 1/3 F D) 1/9 F The force between two charges separated by a distance d is F. If the charges are pulled apart to a distance 3d, what is the force on each charge? QF QFd Q ? Q ? 3d3d3d3d

A) yes, but only if Q 0 is positive B) yes, but only if Q 0 is negative C) yes, independent of the sign (or value) of Q 0 D) no, the net force can never be zero Two balls with charges +Q and +4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q 0 on the line between the two charges such that the net force on Q 0 will be zero? 3R3R +Q+Q +4Q

3R3R +Q+Q – – 4Q Two balls with charges +Q and –4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q 0 anywhere on the line such that the net force on Q 0 will be zero? A) yes, but only if Q 0 is positive B) yes, but only if Q 0 is negative C) yes, independent of the sign (or value) of Q 0 D) no, the net force can never be zero

A proton and an electron are held apart a distance of 1 m and then released. As they approach each other, what happens to the force between them? A) it gets bigger B) it gets smaller C) it stays the same p e

Which of the arrows best represents the direction of the net force on charge +Q due to the other two charges? +2Q +4Q +Q+Q A B C D d d

A) 2 E 0 B) E 0 C) 1/2 E 0 D) 1/4 E 0 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?

+2 +1 dd A)B) C) it’s the same for both Between the red and the blue charge, which experiences the greater electric field due to the yellow charge? +2 +1

+2 +1 dd A)B) C) it’s the same for both Between the red and the blue charge, which experiences the greater electric force due to the yellow charge? +2 +1

Which arrow best represents the electric field at the center of the square? C B A -2 C D) E = 0

What is the direction of the electric field at the position of the X ? D C B A +Q+Q -Q-Q +Q+Q

Field Lines Field lines point in the direction of the Coulomb force on a positive test charge due to the charge creating the field

Electric fields add up vectorially

Asymmetric charge distribution yields asymmetric field

Parallel Plates Constant electric field far away from the top and the bottom Constant direction Constant strength

A) proton B) electron C) both the same p e A proton and an electron are held apart a distance of 1 m and then released. Which particle has the larger acceleration at any one moment?

A proton and an electron are held apart a distance of 1 m and then let go. Where would they meet? A) in the middle B) closer to the electron’s side C) closer to the proton’s side p e

Flux through an Area

Curved Surface and non-uniform Field Changing for every point on surface: –Strength of E –Direction of E –Direction of A

Angle determines sign of flux

What is the Flux through the Surfaces? A1 pos., A2 neg A2 pos., A1 neg Both zero None of the above

A gaussian cylinder is placed in a uniform electric field of magnitude E, aligned with the cylinder axis. For each of the surfaces 1, 2, 3, is the electric flux A. positive, B. negative, or C. zero? E 12 3

A gaussian cylinder encloses a negative charge. For each of the surfaces 1, 2, 3, is the electric flux A. positive, B. negative, or C. zero? 12 3 –Q–Q

A positive charge is located outside a gaussian cylinder as shown. For each of the surfaces 1, 2, 3, is the electric flux A. positive, B. negative, or C. zero? Q+Q

Which statement do you agree with? A. “Since each Gaussian surface encloses the same charge, the net flux through each should be the same.” B. “Gauss’s law doesn’t apply here. The electric field at the Gaussian surface in case B is weaker than in case A, because the surface is farther from the charge. Since the flux is proportional to the electric field strength, the flux must also be smaller in case B.” C. “I was comparing A and C. In C the charge outside the Gaussian surface changes the field over the whole surface. The areas are the same so the fluxes must be different.” D. None of these statements is correct. +Q+Q ABC +Q+Q +Q+Q -6Q

Gauss’s law problem solving 1. Symmetry of charge distributions  Gaussian surface 2. Draw Gaussian surface through point where you want to know E field 3. Determine direction of E field from symmetry of charge distribution 4. Calculate electric flux through Gaussian surface 5. Calculate charge enclosed by surface 6. Solve for E as a function of distance from charge using Gauss’ law

What is the symmetry of a long straight wire with line charge density λ? CylindricalEllipticalSphericalPlanar

What is the symmetry of a non- conducting hollow sphere with charge density ρ? CylindricalEllipticalSphericalPlanar

Which Gaussian surface should we choose to calculate the electric field of a non-conducting hollow sphere with charge density ρ ? CylinderPillboxSphereOther

Which radius should the Gaussian sphere of a non-conducting hollow sphere with charge density ρ have? Less than inner radius of hollow sphere More than outer radius of hollow sphere Between inner and outer radius of hollow sphere Depends on where you are interested in the electric field

Which is the symmetry of a sheet of metal with surface charge density σ? CylindricalEllipticalSphericalPlanar

Which Gaussian surface should we choose to calculate the electric field of a metal sheet with surface charge density σ? CylinderPillboxSphereOther

Which of the three surfaces of the pillbox has a non-zero electric flux? Top (outside conductor) Mantle (half-submerged) Bottom All three

Electric field of a solid charged sphere Choose gaussian surface A 1 to calculate E field outside sphere Choose gaussian surface A 2 to calculate E field inside sphere

Electric field of solid charged sphere

How does the electric field of a long wire depend on R? Not, Const. R1/R 1/R 2

Non-conducting solid cylinder and cylindrical tube, both carry charge density 15μC/m 3 ; R 1 =1/2R 2 =R 3 /3=5cm. Calculate the electric field. Group 1: inside solid cylinder Group 2: between cylinders Group 3: inside hollow cylinder Group 4: outside both cylinders

Electric Field as a function of distance from axis

The analogy of the potential energy of two rocks are charges between charged plates. Which plate should be on top? PositiveNegativeDepends

The analogy of the potential energy of two rocks are charges between charged plates. What does the small rock represent? More charge Less charge Negative charge Depends

The analogy of the potential energy of two rocks are charges between charged plates. What is a correct analogy? Neg. plates up and neg. charges high Neg. plates down and neg. charges high Pos. plates and neg. charges up/high None of the above

What is correct? Potential would be lower at b for negative charges The potential at b is higher for the larger charge Negative charges go from low to high potential None of the above

A proton is moved from position i to position f below. Is the change in its potential energy A. positive, B. negative, or C. zero? +  i  f

In each of the situations shown below, an electron is moved from position i to position f. Is the change in its potential energy A. positive, B. negative, or C. zero? +  i  f 3.  i  f  i  f + -

+ - Draw the field lines & equipotential lines of two charges plates

Draw the field lines & equipotential lines of a point charge +

Draw the field lines & equipotential lines of two opposite point charges +- -

Draw the field lines & equipotential lines of two point charges ++

Four point charges are arranged at the corners of a square. Draw the field lines & equipotential lines Draw the field lines & equipotential lines -Q-Q-Q-Q -Q-Q-Q-Q +Q+Q+Q+Q +Q+Q+Q+Q

Four point charges are arranged at the corners of a square. What are the electric field E and potential V at the center of the square? Draw the field lines & equipotential lines A) E = 0 V = 0 B) E = 0 V  0 C) E  0 V  0 D) E  0 V = 0 -Q-Q-Q-Q -Q-Q-Q-Q +Q+Q+Q+Q +Q+Q+Q+Q

The electric potential is shown at four points in space below. Estimate the electric field (magnitude and direction!) at the dot. 25 V 10 V 15 V 7.1mm

An electron is shot directly towards a 2mm diameter plastic bead with charge –1 nC from very far away. It “reflects” from the bead reaching a turning point 1mm from the surface of the bead. What was the initial speed of the electron? -1 nC 1mm

The potential of a point charge Q is assessed at different distances. Sort the potential starting from the highest. A) V 1cm in front of Q=+2nC B) V 1m behind Q=+2nC C) V 1cm left of Q=-4nC D) V 1m right of Q=-4nC ABCDABDCDCBA None of the above

Equipotential Lines Electric field is perpendicular to equipotential lines –Does this determine its direction fully? –Why is the right plate at 0V?

Point charge Can we calculate how big the charge is? Is it positive or negative?

What would a negative charge change? Shape of equipotential lines Potentials would be negative Potential would increase from center other

Do the distorted circles on the left represent the same potential as the right ones? NoYes Up to a sign Depends

A parallel plate capacitor has plates with area A, separated by a distance d. A battery with voltage V is connected across the plates. For each modification listed, state whether the capacitance A) increases, B) decreases, or C) stays the same. 1. Increase d 2. Increase A 3. Increase V 4. Reverse battery polarity

A parallel plate capacitor has plates with area A, separated by a distance d. A battery with voltage V is connected across the plates. For each modification listed, state whether the capacitance A) increases, B) decreases, or C) stays the same. 1. Increase d  C=ε 0 A/d  C decreases 2. Increase A  C=ε 0 A/d  C increases 3. Increase V  C not function of V (device does not change)  C same Note that charge goes up (Q=CV at constant C), so electric field goes up (E= ε 0 Q/A for plate of charges) [yet it is constant as a function of position!], which is, of course, why the potential difference (V=Ed at constant d) is up. Note that charge goes up (Q=CV at constant C), so electric field goes up (E= ε 0 Q/A for plate of charges) [yet it is constant as a function of position!], which is, of course, why the potential difference (V=Ed at constant d) is up. 4. Reverse battery polarity  same, device does not change

A parallel plate capacitor has plates with area A, separated by a distance d. A battery with voltage V is connected across the plates. For each of the following modifications, state whether the charge on the plate connected to the positive battery terminal A) increases, B) decreases, or C) stays the same. 1. Increase d 2. Increase A 3. Increase V 4. Reverse battery polarity

A parallel plate capacitor has plates with area A, separated by a distance d. A battery with voltage V is connected across the plates. For each of the following modifications, state whether the charge on the plate connected to the positive battery terminal A) increases, B) decreases, or C) stays the same. 1. Increase d  V=const. (same battery), C=ε 0 A/d decreases  Q=CV decreases 2. Increase A  V=const. (same battery), C=ε 0 A/d increases  Q=CV increases 3. Increase V  C=const., so Q=CV increases 4. Reverse battery polarity: Reversing polarity will first decrease charge, so that charge built-up is opposite later.

A parallel plate capacitor has plates with area A, separated by a distance d. A battery with potential difference V is connected across the plates for a long time, and then disconnected. For each of the following modifications, state whether the potential difference between the plates A) increases, B) decreases, or C) stays the same. 1. Increase d 2. Increase A

A parallel plate capacitor has plates with area A, separated by a distance d. A battery with potential difference V is connected across the plates for a long time, and then disconnected. For each of the following modifications, state whether the potential difference between the plates A) increases, B) decreases, or C) stays the same. 1. Increase d  Q=const., C decreases  V=Q/C increases (more voltage needed for same charge) 2. Increase A  Q=const., C increases  V=Q/C decreases (less voltage needed to keep same charge)

Consider a simple parallel-plate capacitor whose plates are given equal and opposite charges and are separated by a distance d. Suppose the plates are pulled apart until they are separated by a distance D > d. The electrostatic energy stored in the capacitor is now A. greater than B. the same as C. smaller than before the plates were pulled apart.

Consider a simple parallel-plate capacitor whose plates are given equal and opposite charges and are separated by a distance d. Suppose the plates are pulled apart until they are separated by a distance D > d. The electrostatic energy stored in the capacitor is now A. greater than B. the same as C. smaller than before the plates were pulled apart. Q=const here, so if d is increased, device changes  C goes down, V goes up, U=1/2 QV goes up. Q=const here, so if d is increased, device changes  C goes down, V goes up, U=1/2 QV goes up.

Consider a simple parallel-plate capacitor which has been fully charged by a battery with potential V and left connected to it. Suppose the plates are pulled apart from their initial separation d to a separation D > d. The electrostatic energy stored in the capacitor is now A. greater than B. the same as C. smaller than before the plates were pulled apart.

Consider a simple parallel-plate capacitor which has been fully charged by a battery with potential V and left connected to it. Suppose the plates are pulled apart from their initial separation d to a separation D > d. The electrostatic energy stored in the capacitor is now A. greater than B. the same as C. smaller than before the plates were pulled apart. Now V=const, charge Q can change. C goes down, so Q=CV goes down, so U=1/2 QV goes down. Now V=const, charge Q can change. C goes down, so Q=CV goes down, so U=1/2 QV goes down.