A charged particle experiences a force when moving through a magnetic field. The force will be at a maximum when the charge is moving perpendicular to the magnetic field lines. The force will be zero when the charge is moving parallel to the magnetic field lines. The formula used to calculate the force on the moving charge is:
F = qvBsinθ
F = magnetic force in Newtons (N)
q = charge of the particle in Coulombs (C)
v = velocity of the particle in m/s
B = magnetic field in Tesla (T)
= angle between the charge and the magnetic field
(Note that if = zero, then F = 0 also and if =90 degrees then F
is at a maximum because the sin of 90 = 1)
Direction of Force, Field, or Velocity (Right-Hand Rule)
Using your right hand, for a positive charge , your fingers point in the direction of the magnetic field. Your thumb points in the direction of the velocity vector. Your palm points in the direction of the force on the moving charge. For a negative charge, reverse the direction of your answer for field, force or velocity (whichever you are asked to find.)
Since there are three vectors that are involved in magnetic force and field problems, there are three axes involved here – the x, y, and z axes. The z-axis is going into and coming out of the page. Positive z is out of the page and negative z is into the page.
- To indicate a direction out of the page, dots are used . . . . (the tip of an arrow)
- To indicate a direction into the page, x’s are used x x x x x (the tail of an arrow)
Description of Motion of Charged Particle in a Magnetic Field
When a charged particle enters a magnetic field, it tends to follow a circular path. Why?
The answer lies in the force that acts on the particle as it moves through the field.
Consider a positive particle that moves through a field that is directed into the page (-z). The force will always be directed toward the center of a circular path. Does this force sound familiar? Centripetal force also acts towards the center of a circle.
Since both a centripetal and magnetic force are present, they must be equal to each other:
- Since Magnetic Force = qvB and Centripetal Force = mv^2/r , then it follows that…
- qvB=mv^2/r OR r = mv/qB. This defines the radius of the circular path when a charged particle enters a magnetic field.
- Notice that mv also equals the momentum of the particle!
- Therefore, the radius is directly proportional to the momentum and inversely related to the strength of the magnetic field and the charge on the particle.