Question

A proton and an electron traveling at the same speed enter a uniform magnetic field. The velocity vector of each particle is perpendicular to the magnetic field. Which of the following statements best describes their motions?

The paths of both particles will curve in the same direction, but the radius of the electron's trajectory will be much larger than the radius of the proton's trajectory.

The paths of both particles will curve in same direction, but the radius of the proton's trajectory will be much larger than the radius of the electron's trajectory.

The paths of both particles will curve in opposite directions, but the radius of the electron's trajectory will be much larger than the radius of the proton's trajectory.

The paths of both particles will curve in opposite directions, but the radius of the proton's trajectory will be much larger than the radius of the electron's trajectory.

Actually, both particles will be unaffected by the magnetic field.

Answer 1

Magnetic force on a charged particle in magnetic field is given by:

F = q*(VxB)

Now direction of force on charged particle is given by right hand rule:

If we point our thumb towards the direction of motion and finger towards the magnetic field, then direction of palm will be direction of force on the positive charge particle and direction of back side of palm will be direction of force on negative charged particle.

And since force is a vector quantity, and since both electron and protons have opposite signs of charge, So both will have force in opposite direction.

Now Using force balance on charged particle in magnetic field

Fc = Fm

m*V^2/R = q*V*B

R = m*V/(q*B)

Since both electrons and protons are traveling with same speed in same magnetic field, So Radius of path will only depend on the ratio of m/q

Since both have same magnitude of charge, So Radius of path will be directly proportional to the mass of particles

Mass of electron = 9.1*10^-31 kg

Mass of proton = 1.67*10^-27 kg

Since mass of proton is much larger than mass of electron, So the radius of the proton's trajectory will be much larger than the radius of the electron's trajectory.

Correct option is D.