Circular Motion of Charges in Magnetic Fields Video Lessons

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Problem: Ions having equal charges but masses of M and 2M are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius R, what is the radius of the arc followed by the lighter?A) 2/⎷2B) R/2C) 3RD) ⎷2RE) 4R

FREE Expert Solution

Work done by the electric force in a moving charge:

W=-qV

Kinetic energy:

K=12mv2

Centripetal force:

Fc=mv2r

Magnetic force on moving charge:

F=qvBsinθ

The kinetic energy of the ions is equal to the work done by the electric force.

|W| = |K|

qΔV = (1/2)mv2 

v = (2qΔV/m)(1/2)

The net force on the ions is due to the magnetic force. 

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Problem Details

Ions having equal charges but masses of M and 2M are accelerated through the same potential difference and then enter a uniform magnetic field perpendicular to their path. If the heavier ions follow a circular arc of radius R, what is the radius of the arc followed by the lighter?
A) 2/⎷2
B) R/2
C) 3R
D) ⎷2R
E) 4R

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