# The motion of a charged particle in a uniform magnetic field

FL  = B q v

• FL       magneticforce  in N
• B      magnetic induction in T
• q      charge particle in C
• v     speed particle in m s-1

Example   1

An electron enters at A in a uniform magnetic field with a speed of  4.0 x 107  m.s-1

The magnetic field has a magnitude of  3.0 x 10-3 T  and the direction is into the paper

The electrons move perpendicular to the magnetic field.

On the electron acts a magnetic force :

FL   = B q  v

FL   = (3.0 x 10-3)( 1.6 x 10-19)( 4.0 x 107) = 1.92 x 10-14 N

The Left-Hand-Rule determines the direction of the magnetic force . (For the description of this rule : see example 1 in the previous paragraph)

The electron goes at A from the left side to the right side.

The direction of the current I is opposite to the direction   of  the velocity of the electron.

So the direction of I is from right to left.

The direction of the magnetic force is downward.

F is perpendicular to the velocity v.

The electron is in a uniform circular motion.

Example 2

Calculate the radius of the path

FL is the centripetal force

FL  = Fc

B q v = (m v2)/r

r = (m v)/(B q)

r = ((9.1 x 10-31 )(  4.0 x 107)) / ((3.0 x 10-3)( 1.6 x 10-19 )) = 7.6 x 10-2 m 