Question

A particle is acclerated from rest through a 4,500 V potential. It then enters a region of uniform magentic field where it traces out a circular orbit with radius 5.46cm. Find the charge-to-mass ratio of the particle. The strength of the magnetic field is 0.500T

Answer 1

the force on particle due to electric field associated to electric potential is

If we assume that the particle is accelerated on horizontal direction along to a distance d, the electric field is

and, if the only force on particle in region where there is a electric potential then it is equal to net force on particle, so according to Newton's second law

so acceleration of the particle is

and its speed when entering to the region of magnetic field

when particle enters a region where there is a magnetic field, a magnetic force is exerted on it. magnetic force on a particle is defined as

but if angle between velocity an magnetic field is

again, if the only force on particle in this region is the magnetic force, this is equal to net force and

where is centripetal acceleration

then,

therefore, as particle has an uniform circular motion its speed is constant

the charge-to-mass ratio of the particle is