Charged particles in magnetic fields

Question 1

What is the equation which gives the force acting on a single charged particle moving through a magnetic field?

Answer 1

F=qvB- Force acting on particle,F- velocity of particle,v- Magnetic field density, B

Question 2

Why do charge particles move in a circular path when the pass through a magnetic field?

Answer 2

By Fleming’s left hand rule the force on a moving charge in a magnetic field is always perpendicular to the motion of travel.

Question 3

When is the effect that charged particles move in circular paths is used and what does the radius of the curvature allow you to know about the particle?

Answer 3

This effect is used in particle accelerators such as cyclotrons and synchrotrons.The radius of curvature of the path of a charged particle moving through a magnetic field gives you information about the particle’s charge and mass.

Question 4

Explain how the radius of the circular path of a charged particle can be calculated using Newton’s second law and F=qvB.

Answer 4

For uniform circular motion Newton’s second law gives:

F = mv²/r

So far a charged particle following a circular path in a magnetic field (where F=qvb) :

qvB = mv²/r

Re-arranging gives:

r = mv/Bq

where r is the radius of the circular path.