An electron and a proton each travel with equal speeds around circular orbits in

Question

An electron and a proton each travel with equal speeds around circular orbits in the same uniform magnetic field, as shown in the diagram to the right (not to scale). The uniform magnetic field is into the page on the diagram. The electron and proton do not affect each other's motion. Which one of the following statements is correct regarding the paths that these two particles take in the magnetic field? a. The electron travels clockwise around the larger circle and the proton travels counterclockwise around the smaller circle. b. The electron travels counterclockwise around the larger circle and the proton travels clockwise around the smaller circle. c. The electron travels clockwise around the smaller circle and the proton travels counterclockwise around the larger circle. d. The electron travels counterclockwise around the smaller circle and the proton travels clockwise around the larger circle. e. The electron travels counterclockwise around the smaller circle and the proton travels counterclockwise around the larger circle.

Explanation / Answer

a) is the correct answer.

we describe the situation by equating centripetal force to magnetic field force

mv^2/r=qvB sin(theta) where theta is the angle between the magnetic field and direction of motion

since these are perpendicular to each other, theta =90 and sin90=1

we have

mv^2/r=qvB or

r= mv/qB

let's look at this equation: the electron and proton have the same charge, so the q's are the same for both; the mag field is the same and we are told the velocity is the same...therefore the only difference is the mass, and since the mass of tge proton is much larger, the radius of the proton orbit will be larger since r is proportional to m

the force on the charged particle is q v cross B which is the cross product between v and B...if you don't know the cross product, use the right hand rule

for a mag field into the plane (-k direction), a positively charged particle will move in the counterclockwise direction...

suppose the proton is moving along the +X axis, then we have

q v cross B has direction;
+ i cross (-k) =-i cross k = k cross i =+j
which means the proton is being deflected in the counterclockwise direction

Hence, electron travels clockwise around the larger circle and proton travels counterclockwise around smaller circle

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