When is there no magnetic force on a moving charge?

When it is stationary or moving parallel to the field.

Why does the magnetic force not change a particle's kinetic energy?

The force is always perpendicular to the velocity, so it does no work.

How do you use Fleming's left-hand rule for a negative charge?

Point the second finger opposite to the velocity, as conventional current is opposite to the motion of negative charge.

What path does a charged particle follow when it moves perpendicular to a uniform magnetic field?

A circle, with the magnetic force providing the centripetal force.

How does the radius change if the speed doubles?

It doubles, as r is proportional to v.

How does the radius change if the field strength doubles?

It halves, as r is proportional to 1/B.

State the time for one revolution of a charged particle in a magnetic field.

T = 2πm/(BQ), independent of the speed.

Why is the radius for an electron smaller than for a proton at the same speed?

The electron has a much smaller mass, so r = mv/(BQ) is smaller.

Why do the particles in a cyclotron spiral outwards?

Their speed increases at each gap crossing, so r = mv/(BQ) increases.

Why can the cyclotron's alternating p.d. have a constant frequency?

The time for a semicircle, πm/(BQ), does not depend on speed.

Moving charges in a magnetic fieldAQA A-Level Physics: Flashcards

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State the equation for the force on a charged particle moving perpendicular to a magnetic field.

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State the equation for the force on a charged particle moving perpendicular to a magnetic field.: F = BQv.
When is there no magnetic force on a moving charge?: When it is stationary or moving parallel to the field.
Why does the magnetic force not change a particle's kinetic energy?: The force is always perpendicular to the velocity, so it does no work.
How do you use Fleming's left-hand rule for a negative charge?: Point the second finger opposite to the velocity, as conventional current is opposite to the motion of negative charge.
What path does a charged particle follow when it moves perpendicular to a uniform magnetic field?: A circle, with the magnetic force providing the centripetal force.
Derive the radius of the circular path.: BQv = mv²/r, so r = mv/(BQ).
How does the radius change if the speed doubles?: It doubles, as r is proportional to v.
How does the radius change if the field strength doubles?: It halves, as r is proportional to 1/B.
State the time for one revolution of a charged particle in a magnetic field.: T = 2πm/(BQ), independent of the speed.
Why is the radius for an electron smaller than for a proton at the same speed?: The electron has a much smaller mass, so r = mv/(BQ) is smaller.
Why do the particles in a cyclotron spiral outwards?: Their speed increases at each gap crossing, so r = mv/(BQ) increases.
Why can the cyclotron's alternating p.d. have a constant frequency?: The time for a semicircle, πm/(BQ), does not depend on speed.

Exam questions on Moving charges in a magnetic field

A beam of protons travels in a vacuum at a speed of 2.0 × 10⁶ m s⁻¹ and enters a region of uniform magnetic field of flux density 0.15 T. The velocity of the protons is at right angles to the field. The charge of a proton is 1.60 × 10⁻¹⁹ C.
Explain why the magnetic force does not change the kinetic energy of a proton.2 marks
In a vacuum chamber, a beam of protons and then a beam of electrons are fired in turn, each at a speed of 4.0 × 10⁶ m s⁻¹, horizontally due east into a region of uniform magnetic field of flux density 2.0 mT directed vertically upwards. The mass of an electron is 9.11 × 10⁻³¹ kg, the mass of a proton is 1.67 × 10⁻²⁷ kg and the magnitude of the charge on each is 1.60 × 10⁻¹⁹ C.
Calculate the radius of the circular path of the electrons.2 marks
A cyclotron accelerates protons. They move in semicircles inside two hollow, D-shaped metal chambers that lie in a uniform magnetic field of flux density 0.80 T, perpendicular to the plane of the semicircles. Each time a proton crosses the gap between the two chambers it is accelerated by an alternating potential difference. The protons spiral outwards and leave the cyclotron at an outer radius of 0.30 m. Proton mass = 1.67 × 10⁻²⁷ kg and charge = 1.60 × 10⁻¹⁹ C.
Explain why the protons move in semicircles inside the chambers, and why the frequency of the alternating potential difference does not need to change as the protons gain speed.3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).