Explain the principle and working of a cyclotron using its schematic sketch. Show that time of revolution of an ion is independent of its speed or radius of its orbit.

**OR**

Derive an expression for the force between two long straight parallel conductors carrying current in sa

Question

Explain the principle and working of a cyclotron using its schematic sketch. Show that time of revolution of an ion is independent of its speed or radius of its orbit.

**OR**

Derive an expression for the force between two long straight parallel conductors carrying current in same direction. Hence define one Ampere.

Accepted Answer

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> [!TLDR]
> A cyclotron accelerates ions using crossed static magnetic field and alternating electric field across a gap; the time for one revolution, T=2πm/(qB), is the same at every radius/speed — this constancy is what lets a fixed-frequency oscillator keep accelerating the ion.
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> **Principle & working:** A cyclotron consists of two hollow D-shaped metal chambers ('dees') placed in a strong uniform magnetic field $B$ perpendicular to their plane, with a small gap between them connected to a high-frequency alternating voltage source. A positive ion, injected near the centre, is accelerated across the gap by th …

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