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 of specific charge (charge/mass) alpha released from origin at time t=0 with velocity vec v = v_0 (hat i + hat j) in uniform magnetic field vec B = B_0 hat i. Coordinates of the particle at time t= pi//(B_0 alpha) are

In uniform magnetic field, if angle between vec(v) and vec(B) is 0^(@) lt 0 lt 90^(@) , the path of particle is helix. Let v_(1) be the component of vec(v) along vec(B) and v_(2) be the component perpendicular to vec(B) . Suppose p is the pitch. T is the time period and r is the radius of helix. Then T = (2pim)/(qB), r = (mv_(2))/(qB), P = (v_(1))T Assume a charged particle of charge q and mass m is released from the origin with velocity vec(v) = v_(0) hat(i) - v_(0) hat(k) in a uniform magnetic field vec(B) = -B_(0) hat(k) . Axis of helix is along

In uniform magnetic field, if angle between vec(v) and vec(B) is 0^(@) lt 0 lt 90^(@) , the path of particle is helix. Let v_(1) be the component of vec(v) along vec(B) and v_(2) be the component perpendicular to vec(B) . Suppose p is the pitch. T is the time period and r is the radius of helix. Then T = (2pim)/(qB), r = (mv_(2))/(qB), P = (v_(1))T Assume a charged particle of charge q and mass m is released from the origin with velocity vec(v) = v_(0) hat(i) - v_(0) hat(k) in a uniform magnetic field vec(B) = -B_(0) hat(k) . Pitch of helical path described by particle is

In uniform magnetic field, if angle between vec(v) and vec(B) is 0^(@) lt 0 lt 90^(@) , the path of particle is helix. Let v_(1) be the component of vec(v) along vec(B) and v_(2) be the component perpendicular to vec(B) . Suppose p is the pitch. T is the time period and r is the radius of helix. Then T = (2pim)/(qB), r = (mv_(2))/(qB), P = (v_(1))T Assume a charged particle of charge q and mass m is released from the origin with velocity vec(v) = v_(0) hat(i) - v_(0) hat(k) in a uniform magnetic field vec(B) = -B_(0) hat(k) . Angle between v and B is

A portion is fired from origin with velocity vec(v) = v_(0) hat(j)+ v_(0) hat(k) in a uniform magnetic field vec(B) = B_(0) hat(j) . In the subsequent motion of the proton

A particle of specific charge q//m = (pi) C//kg is projected from the origin towards positive x-axis with a velocity of 10 m//s in a uniform magnetic field vec(B) = -2 hat K Tesla. The velocity vec V of the particle after time t =1//6 s will be

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

A wire forming one cycle of sine curve is moved in x-y plane with velocity vec(V)=V_(x)hat(i)+V_(y)hat(j) . There exist a magnetic field vec(B)=-B_(0)hat(k) . Find the motional emf decelop across the ends PQ of wire.

An alpha particle moving with the velocity vec v = u hat i + hat j ,in a uniform magnetic field vec B = B hat k . Magnetic force on alpha particle is

A particle of charge q and mass m released from origin with velocity vec(v) = v_(0) hat(i) into a region of uniform electric and magnetic fields parallel to y-axis. i.e., vec(E) = E_(0) hat(j) and vec(B) = B_(0) hat(j) . Find out the position of the particle as a functions of time Strategy : Here vec(E) || vec(B) The electric field accelerates the particle in y-direction i.e., component of velocity goes on increasing with acceleration a_(y) = (F_(y))/(m) = (F_(e))/(m) = (qE_(0))/(m) The magnetic field rotates the particle in a circle in x-z plane (perpendicular to magnetic field) The resultant path of the particle is a helix with increasing pitch. Velocity of the particle at time t would be vec(v) (t) = v_(x) hat(i) + v_(y) hat(j) + v_(z) hat(k)