Question

An ion with a charge of +1 is trapped in the earth's magnetic field. It suddenly picks up 2 electrons, and its charge becomes -1. How doesvitsvmotion change? Assumevthevgain o the 2 electrons does not involve a mechanical force​

Answer 1

The direction of the force changes, so, the ion will now rotate in the opposite direction

Explanation:

The force experienced by a moving charge in a magnetic field is (assuming the motion of the charge is perpendicular to the magnetic field)

$F=qvB$ (1)

where

q is the charge

v is the velocity of the particle

B is the strength of the magnetic field

Moreover, the direction of the force is perpendicular to the motion of the particle: this means that the particle moves in a circular motion under the action of this magnetic force.

Equating this force to the centripetal force,

$qvB=m\frac{v^2}{r}$

Where m is the mass of the particle. So we find that the radius of the orbit (r) is

$r=\frac{mv}{qB}$ (2)

In this problem, an ion with initial charge +1 picks 2 electrons and its charge becomes -1.

- From eq.(1), we notice that since the sign of q changes, the direction of the force changes as well: so, the ion will now rotate in the opposite direction

- Moreover, from eq.(2) we notice that as the absolute value of q does not change, then the radius of the orbit does not change.