### Question Description

Particle Accelerator. A charged particle of mass M with charge

-Q is accelerated in the uniform field E between two parallel charged plates whose separation is D as shown in the figure on the right. The charged particle is accelerated from an initial speed v0 near the negative plate and passes through a tiny hole in the positive plate.

– Derive the formula for the electric field E to accelerate the charged particle to a fraction f of the speed of light c. Express E in terms of M, Q, D, f, c and v0.

– (a) Using the Coulomb force and the kinematic equations.

– (b) Using the work-kinetic energy theorem.

– (c) Using the formula above, evaluate the strength of the electric field E to accelerate an electron from 0.1% of the speed of light to 90% of the speed of light. You need to look up and write down the relevant constants, such as mass of the electron, charge of the electron and the speed of light.

• Must be handwritten

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