A particle of charge `q` and mass `m` is projected from the origin with velocity `v=v_0 hati` in a non uniformj magnetic fiedl `B=-B_0xhatk`. Here `v_0` and `B_0` are positive constants of proper dimensions. Find the maximum positive x coordinate of the particle during its motion.

A particle of mass m and charge + q is projected from origin with velocity vec(V)=V_(0)hati in a magnetic field vec(B)=-(B_(0)x)hatk. Here V_(0) and B_(0) are positive constants of proper dimensions. Find the radius of curvature of the path of the particle when it reaches maximum positive x co-ordinate.

A particle of specific charge alpha is projected from origin with velocity v=v_0hati-v_0hatk in a uniform magnetic field B=-B_0hatk . Find time dependence of velocity and position of the particle.

A particle of specific charge alpha is projected from origin with velocity v=v_0hati-v_0hatk in a uniform magnetic field B=-B_0hatk . Find time dependence of velocity and position of the particle.

A particle of charge 'q' and mass 'm' is projected from the origin with velocity (u_0hati+v_0 hatj) in a gravity free region where uniform electric field -E_0hati and uniform magnetic field -B_0hati exist. Find the condition so that the particle would return to origin at least for once .

A particle of specific charge 'alpha' is projected from origin at t=0 with a velocity vec(V)=V_(0) (hat(i)-hat(k)) in a magnetic field vec(B)= -B_(0)hat(k) . Then : (Mass of particle =1 unit)

A charged particle (q.m) released from origin with velocity v=v_(0)hati in a uniform magnetic field B=(B_(0))/(2)hati+(sqrt3B_(0))/(2)hatJ . Maximum z-coordinate of the particle is

A charged particle (q.m) released from origin with velocity v=v_(0)hati in a uniform magnetic field B=(B_(0))/(2)hati+(sqrt3B_(0))/(2)hatJ . Maximum z-coordinate of the particle is

A charged particle (q.m) released from origin with velocity v=v_(0)hati in a uniform magnetic field B=(B_(0))/(2)hati+(sqrt3B_(0))/(2)hatJ . When z-co-ordinate has its maximum value

A particle of charge per unit mass alpha is released from origin with velocity vec v = v_0 hat i in a magnetic field vec B = -B_0 hat k for x le sqrt 3/2 v_0/(B_0 alpha) and vec B = 0 for x gt sqrt 3/2 v_0/(B_0 alpha) The x-coordinate of the particle at time t(gt pi/(3B_0 alpha)) would be

Choose the correct option: A particle of charge per unit mass alpha is released from origin with a velocity vecv=v_(0)hati in a magnetic field vec(B)=-B_(0)hatk for xle(sqrt(3))/2 (v_(0))/(B_(0)alpha) and vec(B)=0 for xgt(sqrt(3))/2 (v_(0))/(B_(0)alpha) The x -coordinate of the particle at time t((pi)/(3B_(0)alpha)) would be