Question

The mass of a proton is 1840 times that of electron. if an electron and proton are injected in uniform electric field at right angle to the direction of the field, with the same kinetic energy, then

Answer 1

All the two particles have the same amount of charge and therefore experience the same absolute value F of electrostatic force The difference will be in the signs of charge.

at right angles to the field, their paths also have the same curvature, at least at first, but for a more difficult reason.

Centrifugal force is mv²/r, hence a particle with initial kinetic energy E = ½mv² moving with an initial radius of curvature r initially experiences a lateral centrifugal force 2E/r.

Balanced by their common electrostatic force F. Since E and F are the same for both particles, so is their radius of curvature, namely r = 2E/F.

 The electron’s path is sqrt(1840) more curved than the proton’s when they have the same KE.

 The electron will go through the same set of curvatures from 2E/F to zero.