Magnetic Force of a Charge Moving in a Magnetic Field

A magnetic force field exerts a force on a charge in field and these charges in motion constitute an electric current. 

If the strength of the magnetic field called flux densityDensity is the measurement of how tightly a material is packed together i.e. how closely the particles are packed in the material. The tighter the material is packed the more its... More can be represented B and the angle between the magnetic field and the direction of the charged motion is θ, when a force\( \scriptsize \overrightarrow{F}\) is applied at velocity v, then,

\( \scriptsize \overrightarrow{F} = q \overrightarrow{V}\overrightarrow{B} sinθ\)

F = force in newton

V = average velocity of the charge in ms^-1

B = flux induction or magnetic induction in Tesla (T)

q = charge in coulombs

I Tesla =1 weber per m² wm^-2

The expression BVsinθ can be represented as B × V

B × V = BVsinθ

 F = qVBsinθ =q (B × B)

When V and B are parallel in the same direction, θ = 0, then F = 0

When V and B are perpendicular, sinθ = sin 90 = 1, then 

F = qVB

Example

Find the magnetic force experienced by an electron projected into a magnetic field of flux density 20 Tesla with a velocity of 4 x 10⁶ ms^-1  and in a direction of (i) 90° (ii)60° (charge in an electron=1.6 x 10^-19 c)

Solution 

(i) F = qVB = qVBsinθ

=1.6 x 10^-19 x 4 x 10⁶ x 20 x sin 90

= 1.6 x 10^-19 x 4 x 10⁶ x 20

= 6.4 x 10^-13 x 20

= 1.28 x 10^-11 N

(ii) F = qVB sin60

= 1.6×10^-19 x 4 x 10⁶ x sin 60

= 6.4 x 10^-13 x 20 x 0.866

= 1.28 x 10^-11 x 0.866

= 1.11 x 10^-11 N