A negatively charged ion (particle) with mass of 1.6 Times 10^-27 kg is moving w

Question

A negatively charged ion (particle) with mass of 1.6 Times 10^-27 kg is moving with the speed of 100,000 m/s from west to east towards the North Pole. The approximate magnetic strength of the earth's pole is, B = 6 Times 10&^-5 Tesla. This charge was deflected due to the earth's magnetic field. Assume earth's magnetic field is at geographic north. Q = -1.6 Times 10^-19 coulomb, rightarrow V = 100,000 m/s What is the magnetic force due to the moving ion and earth's magnetic field? What is the radius of deflection? What is the direction of the deflected negative ion?

Explanation / Answer

a) Fm = q ( v X B)

Fm = 1.6 x 10^-19 x 100000 x 6 x 10^-5 = 9.6 x 10^-19 N

b)

magnetic force will be perpendicular to the direction of velocity .

(Fm = q ( v X B))

hence particle will move in circular path,

Fm = m v^2 / r

q vB = m v^2 / r

r = mv / qB = (1.6 x 10^-27 x 100000) / (1.6 x 10^-19 x 6 x 10^-5)

r =   16.67 m    (radius of circular path )

c) v = i

q = -ve

B = north to south pole (south to north of earth direction)

B = +j

F = - ( i x j) = -k

downward

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