Question: The position vector r, with respect to a given origin O, of a charged particle of mass m and charge e at time t is

The position vector r, with respect to a given origin O, of a charged particle of mass m and charge e at time t is given by

The position vector r, with respect to a given origin O, of

where E, B, a and ω are constants. The corresponding velocity and acceleration are

a charged particle of mass m and charge e at time t

For the case when B = Bk, show that the equation of motion

is given bywhere E, B, a and ω are constants. The corresponding

is satisfied provided ω is chosen suitably.

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