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

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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

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

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

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is satisfied provided ω is chosen suitably.

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