Charged particles in magnetic fields Cambridge International AS & A Level Physics revision
Not started
Learn it
In plain words
A magnetic field can't speed a charged particle up or slow it down. It can only push it sideways. Keep pushing something sideways at a steady rate and it goes round in a circle, which is how physicists steer beams of particles.
4 things to know
- The force on a charge Q moving at speed v in a field of flux density B is F = BQv sin θ. It is greatest when the charge moves at right angles to the field, and zero when it moves along the field or is at rest.
- The force is always at right angles to the velocity. So it does no work, the speed stays constant, and the particle moves in a circle.
- The magnetic force is the centripetal force: BQv = mv² ÷ r, so r = mv ÷ BQ. A faster or heavier particle makes a bigger circle; a stronger field or a bigger charge makes a tighter one.
- For the direction, use Fleming's left-hand rule with the current finger pointing the way a positive charge is moving. For an electron, point it the opposite way to the motion.
Worked example
An electron moves at 2.0 × 10⁷ m/s at right angles to a magnetic field of flux density 1.0 mT. Find the radius of its path. (Mass of an electron = 9.11 × 10⁻³¹ kg.)
- r = mv ÷ BQ.
- = 9.11 × 10⁻³¹ × 2.0 × 10⁷ ÷ (1.0 × 10⁻³ × 1.60 × 10⁻¹⁹).
- = 0.11 m.
Tips and tricks
- Start circular-path questions by writing "magnetic force = centripetal force".
- For electrons and other negative particles, the force is the opposite way from the one the left-hand rule gives for the direction of motion.
It lands in your notebook with its questions as flashcards.
Charged particles in magnetic fields: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
What is the magnetic force on a charge that is at rest in a magnetic field?
The force needs the charge to be moving.
A charged particle moves at right angles to a uniform magnetic field. What shape is its path?
The force is always at right angles to its velocity.
How much work does a magnetic field do on a charged particle moving through it?
The force is always at right angles to the motion.
The flux density is doubled. What happens to the radius of a charged particle's path?
r = mv ÷ BQ.
A proton and an electron move at the same speed at right angles to the same field. Which follows the bigger circle?
The proton has much more mass, and the same size of charge.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 6 marks. Write your answers on paper, then check them.
Charged particles in magnetic fields
Cambridge International AS & A Level Physics 9702 · 6 marks · papermunch.org
Name ______________________________ Date ______________
Find the force on a proton moving at 3.0 × 10⁶ m/s at right angles to a field of flux density 0.20 T.[2]
Show answerHide answer
9.6 × 10⁻¹⁴ N.
Show that a particle of mass m and charge Q moving at speed v at right angles to a field B follows a circle of radius r = mv ÷ BQ.[2]
Show answerHide answer
The magnetic force provides the centripetal force: BQv = mv² ÷ r. Dividing both sides by v and rearranging gives r = mv ÷ BQ.
Explain why a magnetic field does not change the speed of a charged particle.[2]
Show answerHide answer
The magnetic force is always at right angles to the particle's velocity, so it does no work on the particle. Its kinetic energy, and so its speed, cannot change.
Answers: Charged particles in magnetic fields
- 1. 9.6 × 10⁻¹⁴ N.
- 2. The magnetic force provides the centripetal force: BQv = mv² ÷ r. Dividing both sides by v and rearranging gives r = mv ÷ BQ.
- 3. The magnetic force is always at right angles to the particle's velocity, so it does no work on the particle. Its kinetic energy, and so its speed, cannot change.