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 is fired at an angle theta to a uniform magnetic field directed along the x-axis. During its motionalong a helical path, the particle will

A particle having mass m and charge q is projected with a velocity v making an angle q with the direction of a uniform magnetic field B. Calculate the magnitude of change in velocity of the particle after time t=(pim)/(2qB) .

A charged particle of charge q and mass m is shot into a uniform magnetic field of induction B at an angle theta with the field. The frequency of revolution of the particle

A charged point particle having positive charge q , mass m is projected in x-z plane with a speed v_(0) at an angle theta with the x-"axis" , while another identical particle is projected simultaneously along the y-"axis" from the origin (see figure) with an equal speed v_(0) . An electric field vecE= -E_(0)hatk exists in the x-z plane, while a magnetic field vecB=B_(0)hatk exists in the region y gt 0 ( F_(0) , B_(0) gt 0 ). It is observed that both the particles collide after some time. Assume that the space is gravity free. ( i ) Find the time after which the particles collide and the coordinates of the point of collision. ( ii ) Find the velocity v_(0) and the angle theta in terms of the other variables. ( iii ) What is the maximum value of the z- coordinate of the first particle ?

An electron is projected along positive z-axis, magnetic field is present along y-axis then direction of initial acceleration of the particle is

In a certain region of space, there exists a uniform and constant electric field of magnitude E along the positive y-axis of a coordinate system. A charged particle of mass m and charge -q (qgt0) is projected form the origin with speed 2v at an angle of 60^@ with the positive x-axis in x-y plane. When the x-coordinate of particle becomes sqrt3mv^2//qE a uniform and constant magnetic. field of strength B is also switched on along positive y-axis. z-coordinate of the particle as a function of time after the magnetic field is switched on is

In a certain region of space, there exists a uniform and constant electric field of magnitude E along the positive y-axis of a coordinate system. A charged particle of mass m and charge -q (qgt0) is projected form the origin with speed 2v at an angle of 60^@ with the positive x-axis in x-y plane. When the x-coordinate of particle becomes sqrt3mv^2//qE a uniform and constant magnetic. field of strength B is also switched on along positive y-axis. x-coordinate of the particle as a function of time after the magnetic field is switched on is

In a certain region of space, there exists a uniform and constant electric field of magnitude E along the positive y-axis of a coordinate system. A charged particle of mass m and charge -q (qgt0) is projected form the origin with speed 2v at an angle of 60^@ with the positive x-axis in x-y plane. When the x-coordinate of particle becomes sqrt3mv^2//qE a uniform and constant magnetic. field of strength B is also switched on along positive y-axis. Velocity of the particle just before the magnetic field is switched on is

A particle of mass 'm' and charge 'q' is incident on XZ plane with velocity 'v' in a direction making angle theta with a uniform magnetic field applied along X-axis. The magnetic field applied along X-axis. The nature of motion performed by the particle is

A charged particle of charge Q and mass m moves with velocity v in a circular path due to transverse magnetic field, B, then its frequency is