**IBDP** **Physics**** Long Question Analysis Topic: Physics - Charged Particles**

**Exam Question:**

(a) Deduce an expression for the frequency of revolution of a charged particle in a magnetic field and show that it is independent of velocity or energy of the particle.

(b) Draw a schematic sketch of a cylotron. Explain, giving the essential details of its construction, how it is used to accelerate the charged particles.

**Answer:**

For IBDP Physics, you should know:

(a) First, let's jot down the magnetic force on a charged particle inside a magnetic field. The formula is:

**F = qvB**

This force is** equivalent to the centripetal force** that acts on the particle.

**F = mv**^{2}** / r = qvB**so

**v / r = qB / m**

In addition, frequency is given by:

**f = v / 2πr = qB / 2πm**

From this, we can infer that frequency is** independent of the particle's velocity**.

(b) Refer to the schematics of a cyclotron below:

A cyclotron **accelerates particles to very high speeds**. From a region consisting of orthogonal electric and magnetic fields, protons are injected. Due to the **magnetic field**, the particle experiences a** centripetal force**. Additionally, it feels an **accelerating force **because of the **electric field**.

In a cyclotron, the radius of a particle is found by:

**r = mv / qB**

That being said, the particle's speed can be found using its radius. Then, it can be accelerated to the needed value.

Work hard for your IBDP Physics examination!

End of analysis. Great!