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Lesson 1, Topic 4
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# Magnetic Force of a Charge Moving in a Magnetic Field

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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 density 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

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