In a Millikan-type experiment, the measured charge on each oil drop must be an integer multiple of the elementary charge .
What set of measured charges is consistent with charge quantization?
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Two small charged spheres are separated by a distance in air and exert an electrostatic force of magnitude on each other. The separation is changed to and the spheres are placed in an insulating liquid where the permittivity is three times that of air.
What is the new force magnitude?
A negatively charged plastic rod is brought close to, but does not touch, a neutral metal sphere on an insulating stand. The sphere is then connected briefly to Earth while the rod remains in place. The Earth connection is removed before the rod is taken away.
What is the final charge on the sphere and the charge transfer during earthing?
The sphere is negative; electrons move from Earth to the sphere.
The sphere remains neutral; equal charges move in opposite directions.
The sphere is positive; protons move from Earth to the sphere.
The sphere is positive; electrons move from the sphere to Earth.
A long straight wire is perpendicular to the page and carries conventional current out of the page.
What diagram shows the magnetic field around the wire?
Two point charges, and , are separated by in a vacuum.
What is the electric potential energy of the two-charge system?
The diagram shows equipotential lines in a region of an electric field. Adjacent lines differ by the same potential difference.
At which labelled point is the electric field strength greatest?

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A
B
D
A negatively charged insulating rod is brought close to a neutral conducting sphere on an insulating stand. The sphere is connected briefly to Earth while the rod remains in position. The Earth connection is then removed before the rod is taken away.

Explain why the sphere is left with a net charge and state the sign of this charge.
0
In a Millikan-type experiment, the measured charges on three oil drops are , and .
Deduce the elementary charge from these data and explain how the data support charge quantization.
0
A long straight wire carries a steady conventional current into the plane of the page.

State the direction of the magnetic field around the wire and describe how the field strength changes with distance from the wire.
0
Two parallel metal plates have a potential difference of and are separated by . A particle of charge is between the plates away from edge effects.
What is the magnitude of the electric force on the particle?
Two equal positive point charges are fixed a small distance apart.
What diagram best represents the electric field lines in the plane containing the charges?
Four point charges are fixed at the corners of a square. The charges on one diagonal are and . The charges on the other diagonal are and .
What is the electric potential at the centre of the square?

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, where is the distance from a corner to the centre
, where is the distance from a corner to the centre
It cannot be determined without knowing the directions of the electric fields.
The electric potential varies along the -axis from at to at .
What is the average electric field component between these points?
An electron is moved from a point at electric potential to a point at electric potential .
What is the change in electric potential energy of the electron?
Two small charged spheres are fixed in a liquid of relative permittivity . The charges are and and their separation is .

Calculate the magnitude of the electrostatic force on either sphere and state the direction of the force on the positive sphere.
0
Two large parallel metal plates are separated by . The potential difference between the plates is . A small particle with charge is placed midway between the plates, away from the edges.

Calculate the electric field strength between the plates.
Calculate the force on the particle and state its direction.
0
Two point charges are fixed in a vacuum. The charges are and and their separation is .

Calculate the electric potential energy of the two-charge system and explain the meaning of its sign.
0
Point is from a charge of and from a charge of .

Calculate the electric potential at point due to the two charges.
0
Points and lie on the same equipotential line in an electric field. A small positive charge is moved slowly from to along this line.

Explain why no work is done in moving the charge from to .
0
Three identical metal spheres on insulating stands are used in two electrostatics procedures. The charge on each sphere is measured before and after contact or grounding.

Determine the final charge on each of spheres A and B after they touch and are separated.
State the sign of the final charge on sphere C after the induction procedure.
Explain the role of grounding in the induction procedure shown.
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A pair of large parallel metal plates is connected to a high-voltage supply. A singly charged positive ion is moved from the positive plate to the negative plate through the central uniform region.

Calculate the electric field strength between the plates in the central region.
Determine the electric force on the ion, including its direction.
Determine the energy transferred to the ion as it moves across the full potential difference. Give your answer in joules and in electronvolts.
0
A hollow conducting sphere carries a positive charge and contains no charge inside its cavity. The zero of electric potential is at infinity.
What pair of graphs shows the variation with distance from the centre of the sphere of the electric field strength and the electric potential ?
A hollow conducting sphere has a positive net charge and is in electrostatic equilibrium. The diagram shows a cross-section of the sphere.

Sketch the electric field lines for the sphere, both outside the sphere and inside the hollow region.
0
The graph shows the variation of electric potential with position between two parallel plates. The potential decreases uniformly from at to at .

Determine the electric field strength between the plates, including its direction along the -axis.
0
An electron is moved from a point where the electric potential is to a point where the electric potential is .
Calculate the change in electric potential energy of the electron in joules and in electronvolts.
State whether the electric potential energy of the electron-field system increases or decreases.
0
A hollow conducting sphere of radius carries a charge of . There is no charge inside the hollow region.

State the electric field strength inside the hollow region.
Calculate the electric potential at the centre of the hollow region.
0
Two small conducting spheres carry fixed charges and are placed at different separations. The force sensor records the magnitude of the electrostatic force in air and then with the spheres immersed in an insulating oil.

Describe the relationship between the force in air and the separation of the charged spheres.
Use the air data to determine the magnitude of the charges on the spheres.
Explain why the force readings in the insulating oil are smaller than those in air for the same separation.
0
In a Millikan-type experiment, several oil drops are held stationary between horizontal plates by adjusting the potential difference. The charge calculated for each drop is shown.
| Oil drop | Charge / C |
|---|---|
| 1 | -1.6 Ć 10^-19 |
| 2 | -3.2 Ć 10^-19 |
| 3 | -4.8 Ć 10^-19 |
| 4 | -6.4 Ć 10^-19 |
| 5 | -8.0 Ć 10^-19 |
| 6 | -9.6 Ć 10^-19 |
Use the data to estimate the elementary charge.
Determine the number of excess electrons on the drop with charge .
Explain how these data support the conclusion that charge is quantized.
0
A vertical straight wire passes through a horizontal card. Small plotting compasses are placed at different positions around the wire while a steady conventional current flows.

Determine the direction of the conventional current in the straight wire.
Describe how the magnetic field strength changes with distance from the wire.
Suggest two changes that would increase the magnetic field strength inside the air-core solenoid.
0
The electric potential is measured at different distances from an isolated point charge. The zero of potential is taken to be at infinity.

State the sign of the point charge.
Use the graph to determine the magnitude of the point charge.
Use the tangent to determine the electric field strength at the labelled distance, including direction.
0
A conducting-paper experiment is used to map electric potentials between two metal electrodes of different shapes. Several equipotential lines are drawn from voltmeter readings.

Determine the work done in moving a test charge from Q to R.
State the direction of the electric field at P relative to the equipotential line through P.
Estimate the magnitude of the electric field strength at P.
Explain why the field is strongest near P.
0
A charged hollow conducting sphere is isolated from its surroundings. Measurements of electric field strength are made at different distances from the centre of the sphere.
| Distance from centre / m | Electric field strength / N C^-1 |
|---|---|
| 0.05 | 0 |
| 0.10 | 0 |
| 0.15 | 0 |
| 0.20 | 4500 |
| 0.30 | 2000 |
| 0.40 | 1125 |
State the electric field strength inside the hollow region of the sphere.
Use the external field data to determine the magnitude of the charge on the sphere.
Explain why the field is zero inside the hollow conductor but not zero outside it.
0
Three point charges are fixed at the corners of a triangle. The electric potential energy of the system is found by assembling the charges from infinite separation.

Calculate the electric potential energy of the pair of charges at A and B.
Determine the total electric potential energy of the three-charge system.
Explain the meaning of the negative value for the total electric potential energy.
0
A charged solid conducting sphere is isolated in air. The electric potential is measured along a radial line from the centre of the sphere.

Use the graph to determine the radius of the conducting sphere.
Determine the charge on the sphere.
Use the graph to compare the electric field strength inside the sphere with that just outside its surface.
0
The potential between two parallel plates is measured along a line perpendicular to the plates. Measurements are also taken close to one edge of the plates.

Determine the electric field strength in the central region, including its direction.
Calculate the change in electric potential energy of an electron moved from the negative plate to the positive plate.
Evaluate whether the central value of electric field strength is a valid estimate near the edge of the plates.
0
Two small insulating spheres carry charges and . The centres of the spheres are separated by in air. The spheres may be treated as point charges.

The electrostatic interaction between the two spheres is considered.
Calculate the magnitude of the force on either sphere.
Explain the direction of the force on each sphere.
The spheres are immersed in an oil for which the permittivity is times the permittivity of air. The separation and charges are unchanged. Discuss the effect on the force and on the subsequent motion if the spheres are released from rest.
0
A negatively charged insulating rod is brought near an isolated neutral metal sphere on an insulating stand. A student then connects the sphere briefly to Earth using a conducting wire, removes the wire, and finally removes the rod.

The charging process is analysed.
Explain the distribution of charge on the sphere just before it is connected to Earth.
Explain why the sphere is left with a positive charge at the end of the process.
The student claims that positive charge has been created in the sphere. Evaluate this claim.
0
A hollow conducting sphere is mounted on an insulating support. A small positive charge is placed outside the sphere. No charge is placed inside the hollow cavity.

The electric field in and near the conductor is considered.
State the electric field strength at point B within the conducting material when electrostatic equilibrium has been reached.
Explain why the electric field at the surface of the conductor is perpendicular to the surface.
State the electric field strength at point A in the empty cavity.
Discuss how the field-line pattern outside the conducting sphere differs from that around an isolated positive point charge.
0
A long straight wire, a circular coil and an air-core solenoid each carry a steady conventional current. A small plotting compass is used to investigate the magnetic field patterns.

The magnetic field near the straight wire is considered.
Describe the shape of the magnetic field lines around the straight wire.
Explain how the direction of the magnetic field is determined from the current direction.
State how the spacing of field lines changes with distance from the wire.
Compare and contrast the field pattern of the circular coil with that of the air-core solenoid.
0
A hollow conducting sphere of radius carries a total charge of . There is no charge inside the cavity. The electric potential is defined to be zero at infinity.

The potential of the charged conducting sphere is considered.
Calculate the electric potential at the outer surface of the sphere.
State the electric potential at point A in the cavity.
Explain why no work is done in moving a small test charge slowly from A to B.
Discuss the shapes of the equipotential surfaces inside and outside the charged hollow conductor.
0
Two fixed point charges produce the equipotential pattern shown. A point P is located between the charges, and several field regions are labelled.

Identify the labelled region where the electric field strength is greatest.
Calculate the electric potential at P.
Explain why the electric field at P is not necessarily zero even though the electric potential at P is zero.
0
In a simplified Millikan-type experiment, an oil drop is held stationary between two horizontal parallel plates separated by . The potential difference between the plates is . The effective weight of the drop, including buoyancy correction, is .

The drop is stationary between the plates.
Determine the magnitude of the electric field strength between the plates.
Calculate the charge on the drop.
State the sign of the charge on the drop.
Discuss how repeating this experiment for many oil drops provides evidence for quantization of charge.
0
Two large horizontal parallel plates are separated by and connected to a supply. A small bead of mass carries a charge of . The bead is released from rest close to the negative plate.

Ignore gravitational effects and edge effects.
Calculate the electric field strength between the plates.
Determine the acceleration of the bead immediately after release.
State the direction of the electric field between the plates.
Evaluate the statement: āThe bead gains of kinetic energy in crossing the plates.ā
0
Three point charges are fixed at the vertices of a right-angled triangle. Charge is , charge is and charge is . The distances are , and .

The electric potential energy of the system is to be determined.
State why electric potential energies of the three pairs can be added algebraically.
Calculate the total electric potential energy of the three-charge system.
Interpret the sign of your answer to (a)(ii).
Discuss why using electric potential energy can be more convenient than using forces for this three-charge system.
0
Two fixed point charges lie on a straight line. Charge is at and charge is at . Point lies on the line between the two charges.

Electric potential along the line is considered.
State why electric potential at a point due to the two charges is found by algebraic addition.
Determine the position between the charges where the electric potential is zero.
Evaluate the claim: āAt the point where the electric potential is zero, the electric field strength must also be zero.ā
0
The graph shows the variation of electric potential with position along a line between two large parallel plates. Edge effects are negligible.

Information is obtained from the potential-position graph.
Explain why the electric field between the plates is uniform.
Determine the magnitude and direction of the electric field if the potential decreases by over .
An electron is released from rest near the lower-potential plate. Discuss the changes to the electron's electric potential energy and kinetic energy as it moves.
0
A conducting-paper experiment is used to map the equipotentials between two long, oppositely charged parallel electrodes. The electrodes are separated by and connected to a supply.

The central region between the electrodes is assumed to be uniform.
Determine the electric field strength in the central region.
On the diagram, draw the equipotential line in the central region.
State the angle between electric field lines and equipotential lines.
Evaluate why the measured equipotentials near the ends of the electrodes may not be equally spaced straight lines.
0
Four identical point charges are fixed at the corners of a square of side . The two charges on the left are and the two charges on the right are , where . Point O is at the centre of the square.

The potential and field at O are considered.
Deduce the electric potential at O.
Discuss whether the electric field strength at O is zero.
student sketches equipotential lines for the arrangement and draws one equipotential line crossing another. Evaluate the student's sketch.
0