Force on a Moving Charge in a Magnetic Field

The magnetic field exerts a force on a charge moving in the field because charges in motion constitute an electric current. E.g, the motion of electrons along conducting wires.

The strength of magnetic field, a vector quantity, is represented by Β, called the flux density or magnetic induction. If θ is the angle between the magnetic field direction and the direction of motion of the charges, then, the force, F on the charge is given by:

F=qvBsinθ

This force will be maximum when sin θ = 1 (i. e θ = 90⁰. The charge moves in a direction  perpendicular to the magnetic field)

This force will be zero when θ = 0. (i.e the charge moves in the same direction as the magnetic  field)

Where:

F is force in Newton,N

q is the charge in coulombs,C

v is the average velocity of the charge in m/s

B is the flux density or magnetic induction in tesla, T (1Tesla = 1Weber per m²).

Example:

Find the magnetic force experienced by an electron projected into a magnetic field of flux density  8Tesla with a velocity of 4.0 × 10⁶m/s and in the direction of 60°.

Solution:

F=qvBsinθF=1.6×10−19×4.0×106×8×sin60oF=4.43×10−12N

Note:

1. When an electron is projected perpendicular to the magnetic field, θ=900,∴sinθ=sin90o=1,Hence,F=qvB
2. When an electron is projected parallel to the magnetic field,

θ=0o,∴sinθ=sin0o=0,Hence,F=0

EVALUATION (POST YOUR ANSWERS USING THE QUESTION BOX BELOW FOR EVALUATION AND DISCUSSION):

1. State the formula for calculating the force on a charge moving in a magnetic field.
2. What is the value of F if an electron is projected parallel to the field.

GENERAL EVALUATION (POST YOUR ANSWERS USING THE QUESTION BOX BELOW FOR EVALUATION AND DISCUSSION):

1. Define angle of declination.
2. When F = 0, what is the value of θ and why?
3. What is the value of q?
4. Find the magnetic force experienced by an electron projected into a magnetic field of flux  density 8Tesla with a velocity of 4.0 × 10⁶m/s and in the direction of 40° . Also find F when the  electron is projected normal to the field.
5. A force F projected an electron into a magnetic field of flux density 10 Tesla with a velocity of  2 × 10⁷m/s and normal to the field. (electron charge = 1.6 × 10^-1