A particle of charge and mass is in a uniform electric field of strength .
What is the magnitude of the acceleration of the particle?
A charged particle moves perpendicular to a uniform magnetic field and remains within the field.
What is correct about the speed and kinetic energy of the particle while it is in the magnetic field?
The speed increases but the kinetic energy remains constant.
The speed remains constant but the kinetic energy increases.
Both speed and kinetic energy increase.
Both speed and kinetic energy remain constant.
A positive ion enters the region between two parallel plates with a horizontal velocity. The uniform electric field between the plates is vertically downwards. The ion enters midway between the plates.
Which path is followed by the ion while it is between the plates?
A long straight vertical wire carries a conventional current upwards.
Which diagram shows the direction of the magnetic field around the wire when viewed from above?
An alpha particle of charge moves at in a uniform magnetic field of flux density . The angle between the velocity of the alpha particle and the magnetic field is .
Determine the magnitude of the magnetic force on the alpha particle.
State why the component of velocity parallel to the magnetic field is unchanged.
0
A straight wire of length is placed at right angles to a uniform magnetic field of flux density . The current in the wire is .

Determine the magnetic force on the wire.
State the effect on the force if the direction of the current is reversed.
0
A beam of singly charged ions passes undeflected through perpendicular uniform electric and magnetic fields. The electric field strength is and the magnetic field strength is .
What is the speed of the ions?
A particle with charge magnitude moves at in a uniform magnetic field of flux density . The angle between the velocity and the magnetic field is .
What is the magnitude of the magnetic force on the particle?
Two long parallel wires carry currents in opposite directions. The currents are then both doubled and the separation of the wires is also doubled.
What happens to the force per unit length between the wires?
It remains repulsive and has the same magnitude.
It becomes attractive and doubles in magnitude.
It remains repulsive and doubles in magnitude.
It becomes attractive and is halved in magnitude.
A charged particle enters a uniform magnetic field with velocity at an angle between and to the magnetic field direction.
What is the resulting path of the particle?
A straight line parallel to the field
A circle in a plane perpendicular to the field
A helix with its axis parallel to the field
A parabola in a plane containing the field
A straight horizontal wire carries conventional current to the right. The wire is in a uniform magnetic field directed into the plane of the page.
What is the direction of the magnetic force on the wire?

Downwards
Into the plane of the page
Upwards
Out of the plane of the page
In a mass spectrometer, positive ions pass through a velocity selector and then enter a region containing only a uniform magnetic field. The ions all have the same charge and pass through the selector with the same speed.
What is correct for ions of greater mass in the magnetic-field region?
They are not deflected because the velocity selector has balanced the forces.
They follow the same radius because their speed is the same.
They follow a path of larger radius because their mass-to-charge ratio is larger.
They follow a path of smaller radius because their charge-to-mass ratio is smaller.
An electron enters the uniform electric field between two horizontal parallel plates with an initial horizontal velocity. The upper plate is positive and the lower plate is negative. The potential difference between the plates is and their separation is .

Determine the magnitude of the electric field strength between the plates.
State the direction of the acceleration of the electron while it is between the plates.
Explain why the path of the electron is parabolic while it is between the plates.
0
A proton of speed enters a region of uniform magnetic field of flux density . The velocity of the proton is perpendicular to the magnetic field, which is directed into the page.

State the direction of the magnetic force on the proton at the instant it enters the field.
Determine the radius of the circular path of the proton.
Explain why the kinetic energy of the proton remains constant in the magnetic field.
0
Positive ions pass through a velocity selector. The ions move horizontally to the right through a uniform electric field of strength directed upwards and a uniform magnetic field of flux density directed out of the page.

Determine the speed of ions that pass through undeflected.
State the initial direction of deflection of a positive ion that enters with a smaller speed.
0
Two long parallel wires are separated by . The currents in the wires are and in the same direction.

Determine the force per unit length on either wire.
State whether the force is attractive or repulsive.
0
A proton is accelerated from rest through a potential difference of in a vacuum. After acceleration it enters a second uniform electric field directed opposite to its velocity.
Determine the speed of the proton after it has been accelerated through the potential difference.
Explain why the proton slows down in the second electric field.
0
Electrons enter a uniform electric field between two horizontal parallel plates with initial horizontal speed . The vertical deflection is measured for different lengths of the field region. The initial vertical velocity of the electrons is zero.

Describe what the graph shows about the relationship between and .
Use the graph to determine the vertical acceleration of the electrons in the field.
The polarity of the plates is reversed while the magnitude of the potential difference is unchanged. Explain the effect on the electron beam.
0
A proton enters a region of uniform magnetic field at point P. The magnetic field is directed into the plane of the page. The proton follows the circular path shown.

State the direction of the magnetic force on the proton at P.
Determine the speed of the proton. Use and .
Explain why the kinetic energy of the proton remains constant while it is in the magnetic field.
0
A beam of singly charged positive ions passes through perpendicular uniform electric and magnetic fields. The electric field strength is . The vertical deflection of the beam is recorded for different ion speeds.
| Ion speed / m s^-1 | Vertical deflection / mm |
|---|---|
| 1.8 Ć 10^5 | +4.8 |
| 2.1 Ć 10^5 | +2.4 |
| 2.4 Ć 10^5 | 0.0 |
| 2.7 Ć 10^5 | -2.4 |
| 3.0 Ć 10^5 | -4.8 |
Determine the speed of the ions that pass through undeflected.
Calculate the magnetic field strength in the selector.
Explain why the selected speed is independent of the charge and mass of the ions.
0
Electrons are accelerated from rest through a potential difference and then enter a uniform magnetic field of flux density at right angles. The radius of their circular path is .
What expression gives the specific charge of the electron?
Two long parallel wires are separated by . They carry currents of and in the same direction.
What is the force per unit length between the wires? Use .
, attractive
, repulsive
, repulsive
, attractive
Electrons are accelerated from rest through a potential difference and then enter a uniform magnetic field at right angles to the field. The path in the magnetic field is circular. In one experiment, , and the radius of the path is .

Show that the specific charge of the electron is given by .
Determine the specific charge of the electron from the experimental data.
0
A singly charged positive ion of mass enters a uniform magnetic field of flux density with speed . The velocity of the ion makes an angle of with the direction of the magnetic field.

Explain why the subsequent path of the ion is a helix.
Determine the radius of the helical path.
0
In a mass spectrometer, singly charged positive ions first pass undeflected through a velocity selector. The electric field in the selector is and the magnetic field is . The ions then enter a second region containing only a uniform magnetic field of flux density , where their circular path has radius .

Determine the speed selected by the velocity selector.
Determine the mass of the ion.
State how the radius would change for a heavier isotope with the same charge and the same selected speed.
0
In an investigation of the force on a current-carrying conductor, a straight wire of length is held perpendicular to a uniform magnetic field. The force on the wire is measured for different currents. The best-fit gradient of the graph of force against current is .

Determine the magnetic flux density of the field.
Explain why a straight line through the origin supports the model for this investigation.
0
A straight horizontal wire of length is placed at right angles to a uniform magnetic field. The wire is connected to a variable current supply and the magnetic force on the wire is measured using a balance.

Use the graph to determine the magnetic field strength.
Predict the magnitude of the magnetic force when the current is .
Suggest one advantage of taking readings for both directions of current.
0
Two long parallel wires carry equal currents in the same direction. The force per unit length on one wire is measured for different separations .

State the relationship between the force per unit length and the separation of the wires.
Use the graph to determine the current in each wire. Use .
State the direction of the force between the wires.
0
Positive ions of speed move through a uniform magnetic field of strength . The angle between the ion velocity and the magnetic field is varied.

Explain why plotting the force against gives a straight line.
Use the graph to determine the charge of the ion.
State the force on the ion when it moves parallel to the magnetic field.
0
Two long vertical wires are separated by . Each wire carries a current of upwards. At the location of the experiment, the horizontal component of Earth's magnetic field is .

Determine the magnetic field strength produced by one wire at the position of the other wire.
Explain whether the force between the wires is attractive or repulsive.
Compare the field due to one wire with Earth's horizontal magnetic field and comment on whether Earth's field can be ignored in a precise experiment.
0
Electrons are accelerated from rest through a potential difference and then enter a uniform magnetic field of strength at right angles. Their circular path radius is measured in a fine-beam tube.

State why a graph of against is expected to be linear.
Use the graph to determine the electron charge-to-mass ratio .
Compare the value obtained with the accepted value .
Suggest why the lowest-radius points have the largest fractional uncertainty.
0
A mass spectrometer uses a velocity selector followed by a region containing only a uniform magnetic field. Singly charged positive ions pass undeflected through the selector and then strike a detector at two positions, A and B. The electric field in the selector is and the magnetic field in the selector is . The magnetic field in the analyser region is .

Calculate the speed of ions transmitted by the velocity selector.
Determine the mass of the ion that reaches detector position A. Use .
Use the detector positions to determine the ratio .
Explain why the ion reaching B has the larger mass.
0
Alpha particles enter a uniform magnetic field at an angle to the field direction and follow a helical path. The magnetic field strength is . For an alpha particle, and .

Use the radius of the helix to determine the component of the alpha-particle velocity perpendicular to the magnetic field.
Calculate the time for one complete turn of the helix.
Use the pitch of the helix to determine the component of velocity parallel to the magnetic field.
Explain why the path is helical rather than circular.
0
In a velocity-selector experiment, the magnetic field in the selector is fixed at while the electric field strength is varied. The ions then enter an analyser region where a magnetic field of strength bends the transmitted beam to a detector.
| Electric field / 10^4 V m^-1 | Detector current / a.u. | Analyser radius / m |
|---|---|---|
| 2.60 | 0.07 | 0.260 |
| 2.80 | 0.22 | 0.260 |
| 3.00 | 0.54 | 0.260 |
| 3.10 | 0.81 | 0.260 |
| 3.20 | 1.00 | 0.260 |
| 3.30 | 0.79 | 0.260 |
| 3.40 | 0.53 | 0.260 |
| 3.60 | 0.21 | 0.260 |
| 3.80 | 0.08 | 0.260 |
Determine the electric field strength at which the transmitted ion current is maximum.
Calculate the speed of the ions at maximum transmitted current.
Use the analyser path to determine the mass-to-charge ratio of the ions.
Suggest why the current peak has a finite width rather than occurring at a single value of electric field strength.
0
An electron enters midway between two horizontal parallel metal plates with horizontal speed . The potential difference between the plates is and their separation is . The uniform-field region has length . The upper plate is positive.

Determine the magnitude of the electric field strength between the plates.
Calculate the acceleration of the electron while it is between the plates.
Show that the electron does not strike a plate before leaving the field region.
Explain how the path would change if the electron entered with the same speed but the potential difference was reversed.
0
A proton enters a uniform magnetic field of flux density with speed . The velocity is perpendicular to the field, which is directed out of the plane of the page.

State the initial direction of the magnetic force on the proton.
Explain why the proton follows a circular path while it remains in the field.
Calculate the radius of the circular path.
Evaluate the statement: āThe proton is accelerating in the magnetic field, so its kinetic energy increases.ā
0
A straight wire of length is placed at right angles to a uniform magnetic field of flux density . The wire is connected to a power supply and rests between the poles of a magnet on a sensitive balance. The current in the wire is .

Calculate the magnitude of the magnetic force on the wire.
State one change that would reverse the direction of this force.
Explain why the balance reading changes when the current is switched on.
Evaluate why measurements are often taken for both current directions when determining using this apparatus.
0
Two long straight parallel wires are separated by a fixed centre-to-centre distance of . The currents are varied and the force per unit length is measured. The product of the currents is .

Describe the evidence from the graph that the force per unit length is proportional to .
Use the graph to determine an experimental value for .
Calculate the percentage difference between this value and .
The separation is accidentally measured between the nearest surfaces of the wires rather than between their centres. State the effect on the calculated value of .
0
An electron travels parallel to a long straight wire carrying a steady conventional current of upwards. At the instant shown, the electron is to the right of the wire and has speed upwards. Use and .

Calculate the magnetic field strength at the position of the electron due to the wire.
Calculate the magnitude of the magnetic force on the electron at this instant.
Determine the direction of the magnetic force on the electron.
Explain why the subsequent path of the electron is not a circular arc of constant radius.
0
A beam of singly charged positive ions passes through a velocity selector. The uniform electric field has magnitude and is directed vertically downward. A uniform magnetic field of magnitude is perpendicular to the page. Ions enter the selector horizontally from left to right.

Determine the speed of ions that pass through undeflected.
State the direction of the magnetic field required for the ions in (a)(i) to pass through undeflected.
An ion enters with speed . Explain the initial deflection of this ion.
Discuss whether changing the charge of the ions changes the speed selected by this arrangement.
0
Two long straight parallel wires, and , are separated by . Wire carries a current of and wire carries a current of . The currents are initially in the same direction. A length of wire is in the uniform central region of the apparatus.

State whether the force between the wires is attractive or repulsive.
Calculate the force per unit length on wire .
Determine the total force on the length of wire .
Discuss how a graph could be used to test the dependence of the force on the separation of the wires.
0
A beam of ions is accelerated from rest through a potential difference of and then enters a uniform magnetic field of flux density at right angles to the field. The circular path in the field has radius .

Show that for the ions.
Determine the specific charge of the ions.
Assuming the ions are singly charged, determine their mass in atomic mass units. Use .
Evaluate one reason why measuring a larger radius can improve the reliability of the specific-charge determination.
0
Electrons are accelerated from rest through a potential difference of and then enter a uniform magnetic field of flux density . The angle between the electron velocity and the magnetic field is .

Determine the speed of the electrons as they enter the magnetic field.
Calculate the magnitude of the magnetic force on an electron as it enters the field.
Explain the shape of the path of the electrons in the magnetic field.
Calculate the radius of the helical path. Use your answer to (a)(i),
0
A charged particle leaves a visible track in a cloud chamber placed in a uniform magnetic field of flux density directed into the page. At one point the particle speed is estimated as and the radius of curvature of the track is . The initial velocity at this point is to the right and the track curves upward.

Determine whether the charge of the particle is positive or negative.
Explain your answer to (a)(i).
Determine the magnitude of the charge-to-mass ratio of the particle.
Discuss why the radius of the track may change along the path even though the magnetic field is uniform.
0
Three long parallel wires , and are perpendicular to the page and lie on a straight horizontal line. Wire is between and , from and from . Wires and carry currents out of the page of and respectively. Wire carries a current of into the page.

State the direction of the force on wire due to wire .
Calculate the force per unit length on wire due to wire .
State the direction of the force on wire due to wire .
Determine the magnitude and direction of the resultant force per unit length on wire .
Evaluate why the forces on wires and due to wire do not violate Newton's third law, even though their magnitudes are different.
0
A rectangular coil has turns. Each vertical side of the coil has length and lies in a uniform magnetic field of flux density . A current of flows in the coil. The current in one vertical side is upward and in the other vertical side is downward.

Calculate the magnitude of the force on one vertical side of the coil.
State why the two vertical sides experience forces in opposite directions.
Explain why the coil can rotate even though the net force on it may be zero.
Discuss the effect of reversing the current in the coil.
0
A Bainbridge mass spectrometer uses a velocity selector followed by a uniform magnetic-field analyser. In the selector, and . Singly charged carbon ions then enter an analyser field of flux density at right angles to the field.

Determine the speed selected by the velocity selector.
Calculate the radius of the path of a ion in the analyser. Use .
ion enters the analyser with the same selected speed. Compare the paths of the two isotopes in the analyser.
Evaluate two factors that limit the ability of this spectrometer to resolve the two isotope beams.
0
An alpha particle of charge and mass enters a region of crossed uniform fields. The electric field has magnitude and is directed upward. The magnetic field has magnitude and is directed out of the page. The particle enters horizontally from left to right with speed . The length of the field region is .

Determine the speed for which an alpha particle would pass undeflected through these fields.
Calculate the magnitude of the resultant force on the alpha particle as it enters the field region.
Determine the initial direction of deflection of the alpha particle.
Estimate the vertical deflection of the alpha particle while it is within the field region. Assume the horizontal speed remains approximately constant.
Evaluate the approximation that the horizontal speed remains constant in part (c).
0