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A charged particle q moving in a straigh...

A charged particle q moving in a straight line is accelerated by a potential difference V. It enters a uniform magnetic field B perpendicular to its path. Deduce in terms of V an expression for the radius of the circular path in which it travels.

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To derive the expression for the radius of the circular path of a charged particle moving in a magnetic field, we follow these steps: ### Step 1: Determine the kinetic energy gained by the charged particle When a charged particle \( q \) is accelerated through a potential difference \( V \), it gains kinetic energy equal to the work done on it by the electric field. The kinetic energy \( KE \) gained by the particle is given by: \[ KE = qV \] ...
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