An electron beam travels counterclockwise in a circle of radius R in the magnetic field produced by the Helmholtz coils as shown. If you increase the current in the Helmholtz coils, the electron beam will
A) increase its radius.
B) decrease its radius.
C) maintain the same radius.
D) reverse and travel clockwise with the same radius.
E) reverse and travel clockwise with a larger radius.

Question

An electron beam travels counterclockwise in a circle of radius R in the magnetic field produced by the Helmholtz coils as shown. If you increase the current in the Helmholtz coils, the electron beam will
A) increase its radius. 
B) decrease its radius. 
C) maintain the same radius. 
D) reverse and travel clockwise with the same radius. 
E) reverse and travel clockwise with a larger radius.

Quizplus · Accepted Answer

The direction of the magnetic force on the electron is given by the cross product of the velocity of the electron and the magnetic field. In this case, the direction of the velocity of the electron (counterclockwise) is perpendicular to the direction of the magnetic field (into the page), so the direction of the magnetic force is downward. This force acts as the centripetal force, keeping the electron in its circular path.
 
If the current in the Helmholtz coils is increased, the magnetic field will also increase, and so will the magnetic force on the electron. This means that the centripetal force will also increase, and the electron will need to travel in a smaller radius circle to maintain this balance. Therefore, the electron beam will decrease its radius when the current in the Helmholtz coils is increased. Answer: B.

An Electron Beam Travels Counterclockwise in a Circle of Radius