contestada

An ion with a charge of+ is trapped in the earth's magnetic field. It suddenly picks up 2 electrons, and its charge becomes -1. How does its motion change? Assume the gain of the 2 electrons does not involve a mechanical force.
A. It reverses direction along the same spiral path.
B. It travels along the same spiral path at a greater speed.
C. It travels along the same spiral path at a lesser speed.
D. The rotation of its spiral path reverses direction.

Respuesta :

D. The rotation of its spiral path reverses direction.

Explanation:

  • Magnetic force on a free moving charge is perpendicular to the velocity of the charge and the magnetic field

F = qvB (eq. 1)

where,

q = charge

v = velocity of the particle

B = strength of the magnetic field

  • direction of the force is perpendicular to the motion of the particle
  • the particle moves in a circular motion under the action of this magnetic force.
  • So the force is equal to the centripetal force

[tex]qvB = m\frac{v^{2}}{r}[/tex]

[tex]r = \frac{mv}{qB}[/tex]  (eq. 2)

Where,

m = mass of the particle

r = radius of the orbit

  • An ion with initial charge +1 picks up 2 electrons and its charge becomes -1.
  • From eq.(1), when the sign of q changes, the direction of the force changes
  • So, the ion rotates in the opposite direction
  • From eq.(2),  the value of q does not change, so the radius of the orbit does not change.
  • Therefore, the rotation of its spiral path reverses direction

Otras preguntas