Question

a particle of specific charge is projected from the origin toward positive x-axis with a velocity of 10 m/s in a uniform magnetic field B=-2k the velocity of the particle after time t = 1/6 sec will be

Answer 1

In Y direction the electric field E exist

so the force due to electric field on the charge is given by

Now the acceleration of the charge is given by

now the acceleration is opposite to the direction of velocity

so it will return to origin if displacement in y direction is zero

now due to magnetic field it will move in circular path

time period of its circular motion is given by

now if complete N number of rounds in above time of return then

so here above value must be an integer so that it complete integral nuymber of rounds

so above condition is must to return at origin