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The working of a betatron is NOT based on which of the following principles?

1. Beta particles are emitted in radioactive decay processes.
2. A changing magnetic flux induces an electric field.
3. A charged particle at rest can be accelerated only by an electric field.
4. A magnetic field exerts a force on moving charges that is perpendicular to both the field and the particle's velocity.

Correct answer: Beta particles are emitted in radioactive decay processes.

Solution

A betatron accelerates electrons by the electric field induced from a time-varying magnetic flux (Faraday's law), and the magnetic field provides the centripetal force keeping electrons in a circular path (Lorentz force perpendicular to v and B). It also relies on the fact that charges are accelerated by electric fields. It does NOT rely on radioactive beta decay - electrons are supplied and accelerated electromagnetically, not produced by nuclear decay. So the principle not involved is 'beta particles are emitted in radioactive decay.'

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