A particle of charge `q_(0)` and of mass `m_(0)` is projected along the `y`-axis at `t=0` from origin with a velocity `V_(0)`. If a uniform electric field `E_(0)` also exist along the `x`-axis, then the time at which debroglie wavelength of the particle becomes half of the initial value is:

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 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)

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)

A particle of charge q and mass m enters a region of a transverse electric field of E_(0)hatj with initial velocity v_(0)hati . The time taken for the change in the de Broglie wavelength of the charge from the initial value of lambda_(0) to lambda_(0)//3 is proportional to

A charged particle having charge 2q and mass m is projected from origin in X-Y plane with a velocity v inclined at an angle of 45^@ with positive X-axis in a region where a uniform magnetic field B unit exists along +z axis. The coordinates of the centre of the circular path of the particle are

A charged particle having charge 2q and mass m is projected from origin in X-Y plane with a velocity v inclined at an angle of 45^@ with positive X-axis in a region where a uniform magnetic field B unit exists along +z axis. The coordinates of the centre of the circular path of the particle are

A particle of charge q and mass m is subjected to an electric field E=E_(0)(1-ax^(2)) in the x - direction, where a and E_(0) are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :

A particle of charge q and mass m is subjected to an electric field E=E_(0)(1-ax^(2)) in the x - direction, where a and E_(0) are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :