# 17.3 Motion of a charged particle in a magnetic field

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## Motion of a charged particle in a magnetic field

When a charged particle moves through a magnetic field it experiences a force. For a particle that is moving at right anglesto the magnetic field, the force is given by:

$F=qvB$

where $q$ is the charge on the particle, $v$ is the velocity of the particle and $B$ is the magnetic field through which the particle is moving. Thsi force is called the Lorentz force.

An electron travels at $150\mathrm{m}.{\mathrm{s}}^{-1}$ at right angles to a magnetic field of 80 000 T. What force is exerted on the electron?

1. We are required to determine the force on a moving charge in a magnetic field

2. We can use the formula:

$F=qvB$
3. We are given

• $q=1,6×{10}^{-19}\mathrm{C}$ (The charge on an electron)
• $v=150\mathrm{m}.{\mathrm{s}}^{-1}$
• $B=80\phantom{\rule{3.33333pt}{0ex}}000\mathrm{T}$
4. $\begin{array}{ccc}\hfill F& =& qvB\hfill \\ & =& \left(1,6×{10}^{-19}\mathrm{C}\right)\left(150\mathrm{m}.{\mathrm{s}}^{-1}\right)\left(80\phantom{\rule{3.33333pt}{0ex}}000\mathrm{T}\right)\hfill \\ & =& 1,92×{10}^{-12}\mathrm{N}\hfill \end{array}$
The direction of the force exerted on a charged particle moving through a magnetic field is determined by using the Right HandRule.

Point your first finger (index finger) in the direction of the velocity of the charge, your second finger (middle finger) in the direction of the magnetic field and then your thumb will point in the direction of the force exerted on the charge. If the charge is negative, the direction of the forcewill be opposite to the direction of your thumb.

## Real-world applications

The following devices use the movement of charge in a magnetic field

• old televisions (cathode ray tubes)
• oscilloscope

## Research project : real-life applications of charges moving in a magnetic field

Choose one of the following devices and do some research on the internet or in a library how your device works.

• oscilloscope
• television

## Lorentz force

1. What happens to a charged particle when it moves through a magnetic field?
2. Explain how you would use the Right Hand Rule to determine the direction of the force experienced by a charged particle as it moves in a magnetic field.

## Summary

1. Electromagnetism is the study of the properties and relationship between electric currents and magnetism.
2. A current-carrying conductor will produce a magnetic field around the conductor.
3. The direction of the magnetic field is found by using the Right Hand Rule.
4. Electromagnets are temporary magnets formed by current-carrying conductors.
5. Electromagnetic induction occurs when a changing magnetic field induces a voltage in a current-carrying conductor.
6. Transformers use electromagnetic induction to alter the voltage.
7. A moving charged particle will experience a force in a magnetic field.

## End of chapter exercises

1. State the Right Hand Rule to determine the direction of a magnetic field around a current carrying wire and the Right Hand Rule to determine the direction of the force experienced by a moving charged particle in a magnetic field.
2. What did Hans Oersted discover about the relationship between electricity and magnetism?
3. List two uses of electromagnetism.
4. Draw a labelled diagram of an electromagnet and show the poles of the electromagnet on your sketch.
5. Transformers are useful electrical devices.
1. What is a transformer?
2. Draw a sketch of a step-down transformer.
3. What is the difference between a step-down and step-up transformer?
4. When would you use a step-up transformer?
6. Calculate the voltage on the secondary coil of a transformer if the voltage on the primary coil is 22 000 V and the ratio of primary windings to secondary windings is 500:1.
7. You find a transformer with 1000 windings on the primary coil and 200 windinds on the secondary coil.
1. What type of transformer is it?
2. What will be the voltage on the secondary coil if the voltage on the primary coil is 400 V?
8. An electron moving horizontally in a TV tube enters a region where there is a uniform magnetic field. This causes the electron to move along the path (shown by the solid line) because the magnetic field exerts a constant force on it. What is the direction of this magnetic field?
1. upwards (towards the top of the page)
2. downwards (towards the bottom of the page)
3. into the page
4. out of the page

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