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one is positive, the one is positive, the other is negative other is negative both are positive both are positive both are negative both are negative both are positive or both are positive or both are negative both are negative Two charged balls are Two charged balls are repelling each other repelling each other as they hang from the as they hang from the ceiling. What can ceiling. What can you say about their you say about their charges? charges?

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Two charged balls are repelling each other as they hang from the ceiling. What can you say about their charges? one is positive, the other is negative both are positive both are negative both are positive or both are negative

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

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:A) positiveB) negativeC) positive or neutralD) negative or neutral

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?

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?

If we increase one charge to 4Q, what is the magnitude of F1?A) 3/4 NB) 3.0 NC) 12 ND) 16 N

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?A) 9 FB) 3 FC) 1/3 FD) 1/9 F

Two balls with charges +Q and +4Q are fixed at a separation distance of 3R. Is it possible to place another charged ball Q0 on the line between the two charges such that the net force on Q0 will be zero?A) yes, but only if Q0 is positiveB) yes, but only if Q0 is negativeC) yes, independent of the sign (or value) of Q0D) 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 Q0 anywhere on the line such that the net force on Q0 will be zero?A) yes, but only if Q0 is positiveB) yes, but only if Q0 is negativeC) yes, independent of the sign (or value) of Q0D) 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 biggerB) it gets smallerC) it stays the same

Which of the arrows best represents the direction of the net force on charge +Q due to the other two charges?

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?A) 2 E0B) E0C) 1/2 E0D) 1/4 E0

Between the red and the blue charge, which experiences the greater electric field due to the yellow charge?+1+1ddA)

B)

C) its the same for both

Between the red and the blue charge, which experiences the greater electric force due to the yellow charge?+1+1ddA)

B)

C) its the same for both

Which arrow best represents the electric field at the center of the square?CBA-2 C-2 CD) E = 0

What is the direction of the electric field at the position of the X ?

DCBA+Q-Q+Q

Field LinesField 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 PlatesConstant electric field far away from the top and the bottom Constant directionConstant strength

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) protonB) electronC) both the same

A proton and an electron are held apart a distance of 1 m and then let go. Where would they meet?A) in the middleB) closer to the electrons sideC) closer to the protons side

Flux through an Area

Curved Surface and non-uniform FieldChanging for every point on surface:Strength of EDirection of EDirection of A

Angle determines sign of flux

What is the Flux through the Surfaces?A1 pos., A2 negA2 pos., A1 negBoth zeroNone 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 positive, negative, orzero?E123

A gaussian cylinder encloses a negative charge. For each of the surfaces 1, 2, 3, is the electric flux positive, negative, orzero?123Q

A positive charge is located outside a gaussian cylinder as shown. For each of the surfaces 1, 2, 3, is the electric flux positive, negative, orzero?123

Which statement do you agree with? Since each Gaussian surface encloses the same charge, the net flux through each should be the same.Gausss law doesnt 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.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.None of these statements is correct.

Gausss law problem solvingSymmetry of charge distributions Gaussian surfaceDraw Gaussian surface through point where you want to know E fieldDetermine direction of E field from symmetry of charge distributionCalculate electric flux through Gaussian surfaceCalculate charge enclosed by surfaceSolve 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 ?CylindricalEllipticalSphericalPlanar

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

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

Which radius should the Gaussian sphere of a non-conducting hollow sphere with charge density have?Less than inner radius of hollow sphere More than outer radius of hollow sphereBetween 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 ?CylindricalEllipticalSphericalPlanar

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

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

Electric field of a solid charged sphereChoose gaussian surface A1 to calculate E field outside sphereChoose gaussian surface A2 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/R1/R2

Non-conducting solid cylinder and cylindrical tube, both carry charge density 15C/m3; R1=1/2R2=R3/3=5cm. Calculate the electric field.Group 1: inside solid cylinderGroup 2: between cylindersGroup 3: inside hollow cylinderGroup 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?Positive NegativeDepends

The analogy of the potential energy of two rocks are charges between charged plates. What does the small rock represent?More chargeLess chargeNegative chargeDepends

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 highNeg. plates down and neg. charges highPos. plates and neg. charges up/highNone of the above

What is correct?Potential would be lower at b for negative chargesThe potential at b is higher for the larger chargeNegative charges go from low to high potentialNone of the above

A proton is moved from position i to position f below. Is the change in its potential energypositive,negative, orzero? 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 energypositive,negative, orzero?

2.

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

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 linesA) E = 0 V = 0B) E = 0 V 0C) E 0 V 0D) E 0 V = 0

The electric potential is shown at four points in space below. Estimate the electric field (magnitude and direction!) at the dot.25 V10 V10 V15 V7.1mm

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 nC1mm

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=+2nCB) V 1m behind Q=+2nCC) V 1cm left of Q=-4nCD) V 1m right of Q=-4nC

ABCDABDCDCBANone of the above

Equipotential LinesElectric field is perpendicular to equipotential linesDoes this determine its direction fully?Why is the right plate at 0V?

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

What would a negative charge change?Shape of equipotential linesPotentials would be negativePotential would increase from centerother

Do the distorted circles on the left represent the same potential as the right ones?NoYesUp to a signDepends

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.Increase dIncrease AIncrease VReverse 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.Increase d C=0 A/d C decreasesIncrease A C=0 A/d C increasesIncrease 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= 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. 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.Increase d Increase AIncrease VReverse 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.Increase d V=const. (same battery), C=0 A/d decreases Q=CV decreasesIncrease A V=const. (same battery), C=0 A/d increases Q=CV increasesIncrease V C=const., so Q=CV increasesReverse 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.Increase dIncrease 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.Increase d Q=const., C decreases V=Q/C increases (more voltage needed for same charge)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 nowgreater than the same as 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 nowgreater than the same as 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.

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 nowgreater than the same as 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 nowgreater than the same as 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.

[CORRECT: D ANSWER]

Answer: 5. The magnitude of the electrostatic force exerted by 2 on 1 is equal to the magnitude of the electrostatic force exerted by 1 on 2. If the charges are of the same sign, the forces are repulsive; if the charges are of opposite sign, the forces are attractive.

[CORRECT 5 ANSWER]

Charge doubled: E -> 2 EDistance doubled: E-> ESo E-> E CThe field is a property of the yellow charge and does not change CElectric force is charge of probe times E-field, so +2 experiences more force BBoth electric fields are towards the charges, so the y components cancel, only x component survives and is negative BPositive charges add up in direction D, negative charge pulls in direction B, but weaker due to larger distance D is correct.****Depends on charge of rock: negative charge will fall from low to high el. Potential, but from high to low potential energy.More charge the sign will depend on the electric field direction, but it will always represent more chargeABDC, positive charge is at higher potential, the farther you are from a neg charge, the higher the potential.Potential of a negative charge increases with distance, but is not necessarily negative, since we can shift it by an arbitrary amount.Depends, since you can add a constant so that the potential in the middle is not necessarily zero; if it is the potentials are equal and opposite. *C=eps A/d, not affected by V or reversing polarity*C=eps A/d, not affected by V or reversing polarity*Q=CV, and C= eps A/d. Reversing polarity will first decrease charge, so that charge built-up is opposite later.*Q=CV, and C= eps A/d. Reversing polarity will first decrease charge, so that charge built-up is opposite later.*-Increasing d separates charges more, but electric field is constant, so V grows as distance grows: V= int E dl-increasing A spreads out the charges, so sigma goes down, so E and V go down.*-Increasing d separates charges more, but electric field is constant, so V grows as distance grows: V= int E dl-increasing A spreads out the charges, so sigma goes down, so E and V go down.***Charges will adjust to new situation: V const, d increases, that means E (and Q) decreases, that means less energy is stored.*Charges will adjust to new situation: V const, d increases, that means E (and Q) decreases, that means less energy is stored.