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# Particles in Magnetic Fields

Did you know that magnetism allows the magnetron, and hence, the microwave oven to function? Before the invention of the microwave oven, however, magnetrons were actually in use for radar systems throughout World War Two!  Microwaves are electromagnetic waves with wavelengths between a millimetre and a metre. They can be artificially generated by a device called a magnetron, which forces…

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# Particles in Magnetic Fields

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Did you know that magnetism allows the magnetron, and hence, the microwave oven to function? Before the invention of the microwave oven, however, magnetrons were actually in use for radar systems throughout World War Two! Microwaves are electromagnetic waves with wavelengths between a millimetre and a metre. They can be artificially generated by a device called a magnetron, which forces fast-moving electrons to travel in circular paths. It isn't easy to force something as small as electrons to move in a circle, but it is possible if we apply a magnetic field to them. When charged particles move through a magnetic field, the interaction creates a magnetic force on the particle that causes it to deflect. In this article, we explore the physics at work to produce the force on a charged particle, analyse how this affects the motion of particles in a magnetic field and finally look at the behaviour of some different types of particles.

As we know, electricity and magnetism are sections of physics that seem different but are related through the field of electromagnetism. This is a branch of physics that studies electromagnetic force, which is one of the four fundamental forces of nature and affects the interaction between electrically charged particles.

Maxwell's equations describe how electric and magnetic fields are generated together and constantly interact and affect each other. However, this is beyond what you need to understand for your GCSE exams!

## Magnetic force and magnetic field definitions

Experimentally, it was discovered that when electric charges are moving (that is, they have non-zero velocity), another contribution to the force the charged particles experienced was measured in addition to the electric force, which was already known. This mystery force was the electromagnetic force (also called magnetic force), caused by the movement of charge carriers through some externally applied magnetic field.

A simple experiment you can do at home to observe the effect of the magnetic force uses a strip of aluminium foil, a battery, and a horseshoe magnet. Initially, the magnet should produce no force on the foil strip, as it is made out of aluminium. However, if we create a circuit by attaching each end of the foil strip to the battery terminals, there are now electrons (charged particles) flowing through the foil. If we now bring the strip close to the magnetic field, it will deflect! This demonstrates that a magnetic force is generated by the movement of the charged particles through the magnetic field, as the force disappears when we disconnect the foil circuit and the particles stop moving.

A magnetic force is the force felt by a charged particle (electron, proton, ion, etc.) when it moves through a magnetic field.

Magnetic force is measured in newtons$\left(\mathrm{N}\right)$just like any other force. It is also important to note that the charged particle must be moving relative to the magnetic field to experience a magnetic force.

We must now uncover how magnets create this force, and for this, we need to discuss the magnetic field. The definition of the magnetic field is as follows.

A magnetic field is a region in space where a moving charge or permanent magnet feels a force.

A magnetic field is present at any point in space where a moving charged particle feels a force. The strength of a magnetic field is usually called the magnetic flux density or magnetic field strength and is given the symbol$B.$The unit of measurement of the magnetic field is the Tesla$\left(\mathrm{T}\right)$, which is equivalent to newtons-per-ampere-per-metre,${\mathrm{NA}}^{-1}{\mathrm{m}}^{-1}$.

A Magnetic field doesn't always have a constant strength or flux density. Fields are usually represented by drawing magnetic field lines that extend from the north to south pole of the magnet, with the field strength being greatest where the lines are closest together. Generally, this results in fields being stronger closer to the poles of a magnet and getting weaker with increasing distance.

## Charged particles in a magnetic field

As we've learnt in the topic of electricity, the flow of positive electric charges constitutes a conventional electric current. Therefore, electric currents will experience a force when in a magnetic field. If we think about the electrons moving in circles in a magnetron, as we mentioned at the beginning of the article, how can we be sure that the electrons will move in that way, since they are not contained within a wire? It turns out that there is a relationship between the directions of the magnetic field, the magnetic force and the current. If we know the direction of any two of these quantities, we can find the direction of the third.

### The left-hand rule

The way to determine the direction of the force that a moving charge will feel when it enters a magnetic field is by using Fleming's left-hand rule. The left-hand rule states that you should spread your thumb, index finger and middle finger so that they are all at right angles to each other (as shown in the diagram below).

1. Point your index finger in the direction of the magnetic field$B$, that is, north pole to south pole.
2. Your middle finger gives the direction of conventional current$I$(the movement of positive charge).
3. Your thumb will point in the direction of the force$F$on the particle.

The left-hand rule is used to determine the direction of the force felt by a charged particle when it moves through a magnetic field at right angles to it. Wikimedia Commons CC BY-SA 4.0

### The force on charged particles in a magnetic field

The general law governing the behaviour of an electric charge in the presence of an electromagnetic field is known as the Lorentz force. The general expression also includes the effect of an external electric field, but here we will restrict it to situations where there is only a magnetic field present.

The expression for the force exerted on a charged particle moving perpendicularly through a magnetic field is given by:

$\begin{array}{rcl}\mathrm{Magentic}\mathrm{force}& =& \mathrm{charge}×\mathrm{speed}×\mathrm{magnetic}\mathrm{field}\mathrm{strength}\\ F& =& qvB\end{array}$

where$q$is the charge of the particle,$v$is the magnitude of its velocity (its speed), and$B$is the magnetic field strength.

This equation gives a clear indication that the particle must be moving$\left(v\ne 0\right)$for the magnetic force to be felt at all. We have a relationship in which the direction of the motion, force and field are all at right angles to each other and can be determined by using the left-hand rule.

If the charged particle moves through the magnetic field non-perpendicularly, it still experiences a force - however, this will be less than the maximum force experienced when the two vectors are at right angles. By adding a$\mathrm{sin}\left(\theta \right)$term to the equation, where$\theta$is the angle between the magnetic field and velocity vector of the particle, the magnetic force equation becomes:

$F=qvB\mathrm{sin}\left(\theta \right)$

## The circular motion of charged particles in a magnetic field

We've seen that a charged particle will experience a force that is perpendicular to its direction of motion when it enters a magnetic field at right angles to the field. This means that the particle's direction of motion will change as the magnetic force deflects the particle. As the charged particle has now changed direction, this constitutes a change in direction of the current. If the field remains constant, but the current is changing direction, then the magnetic force generated must also constantly be changing direction! This makes for a confusing scenario but explains how a charged particle in a magnetic field can move along a circular path.

Let's not get too confused and try to understand what's happening by considering the figure below as an example.

1. Imagine an electron moving with a constant speed in a uniform magnetic field pointing into the page (indicated by this symbol ⊗).
2. As the electron moves in the field, it experiences a force which will act at right angles to the velocity. The electron's path curves slightly, and its velocity now has a different direction. However, the velocity is still at a right-angle to the magnetic field direction.
3. The force and velocity are still at right angles to each other and remain in the same plane. In fact, the magnetic force points towards the centre of the circular path the electron is moving along.
4. This continues, with the force and velocity always perpendicular. If we remember from motion in a circle, we have circular motion if these two quantities are perpendicular with constant magnitudes.

This image shows a negatively charged particle, such as an electron, moving in a magnetic field. The force on the particle is constantly changing direction but is constant in magnitude, as is the velocity. Since the two quantities are always perpendicular, the electron moves in a circle, Wikimedia Commons CC 4.0

We determine the direction of the force using the left-hand rule. Electrons are negatively charged, which means that the current is opposite to the direction of the electron's motion.

Considering a setting like the one depicted in the diagram below of the electron in the magnetic field does not allow the particles to be forced into a circular trajectory. This happens for two reasons:

1. The particle initially starts moving along a circular path, but escapes the lower part of the plane because the magnetic field ends. This can be solved by extending the magnetic field in that direction.
2. If the magnetic field is extended in the direction mentioned in point 1, the particle would escape the region to the left side after completing one half-circle. This would happen in any scenario where a particle passes into a magnetic field region: the particle will escape after moving around half a circle.
3. To force the particle to move in a circle, the magnetic field must be externally applied once the particle is already within its region. The magnetic field area must also be large enough to encompass the entire circular path the charged particle will travel along.

An electron will move in a circular path if it enters a uniform magnetic field with constant velocity. It will cease its circular motion if it exits the region containing the magnetic field, which occurs at the bottom of this diagram. StudySmarter Originals.

## Types of particles in magnetic fields

We have seen how electrons are deflected by magnetic fields but we can observe similar deflections for other particles. Here we will look at three of these particles; the alpha particle, the beta particle and the gamma particle.

### Alpha, beta and gamma particles in a magnetic field

We know, from atoms and radiation, that alpha particles are helium nuclei (they contain two neutrons and two protons, making them positively charged). They are also quite heavy, at least compared to the electron, meaning a greater magnetic force is needed to deflect them by the same amount.

Beta particles are fast-moving electrons and so exhibit the same deflection behaviour that we have seen previously. The figure below shows the difference between how an alpha particle and a beta particle are deflected by the same, uniform magnetic field as they move through it.

Gamma particles are high-energy photons emitted during radioactive decay. They are often emitted alongside alpha and beta particles. The big difference, however, is that they are photons and hence uncharged. They will not be deflected by a magnetic field. The diagram below shows the paths of alpha, beta and gamma particles as they move, initially in a straight line, into a region containing a magnetic field.

Alpha and beta particles will be deflected if they move into a region with a magnetic field. The particles deflect in opposite directions since they are oppositely charged. The alpha particle deflects less because it is much heavier than the beta particle. The gamma particle is not deflected in the magnetic field since it is uncharged. StudySmarter Originals

The alpha particle deflects to a lesser amount even though it has a greater charge than the beta particle. This is because it is heavier (it has a greater mass) and the force has a harder time deflecting it. The two particles deflect in opposite directions due to their charges having opposite signs (alpha particles are positive and beta particles are negative), producing magnetic forces in opposite directions. The gamma particle does not interact with the magnetic field and passes through the region undeflected.

## Particles in Magnetic Fields - Key takeaways

• A magnetic force is the force felt by a charged particle (electron, proton, ion, etc.) when it moves through a magnetic field.

• A magnetic field is a region in space where a moving charge or permanent magnet experiences a force.

• Both the charge and the movement of the particle are necessary for the field to exert a force.

• The force$F$exerted by a magnetic field of strength$B$on a particle with charge$q$, moving with speed$v$is found using the below formula. The force direction is perpendicular to the direction of motion of the particle and the magnetic field and is given by:

$\begin{array}{rcl}F& =& qvB\end{array}$

• A moving charged particle in a region where there is a uniform magnetic field travels along a circular trajectory.

• The force on the particle and its speed remain constant when it is moving in a circle in a magnetic field.

• Alpha particles and beta particles will deflect upon entering a magnetic field since they are charged particles.

• Alpha particles deflect less than beta particles due to their greater mass.

• Alpha and beta particles deflect in opposite directions upon entering the same magnetic field since they have opposite charges.

Yes, charged particles that have a velocity in a region where there is a magnetic field are affected by it because they experience a force that is given by the Lorentz force.

Charged particles create a magnetic field when they have a velocity as is predicted by the classical laws of electromagnetism. In general, electric currents create magnetic fields and moving charged particles can be interpreted as anomalous pointlike currents.

Charged particles move in magnetic fields according to Lorent's Law. If the magnetic field has a constant value in the region where the charged particle enters with non-zero velocity, the charged particles describe circles.

Protons are charged particles, meaning they can create a magnetic field if they have a velocity.

Particles moving in a region where there is a magnetic field do not follow the magnetic field lines since the force exerted on them is always perpendicular to their velocity AND the magnetic field.

## Particles in Magnetic Fields Quiz - Teste dein Wissen

Question

An electric charge generates an electric field. If it moves, a magnetic field appears too.

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Question

Magnetic fields are measured in Teslas.

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Question

A magnetic force is the force felt by a charged particle (electron, proton, ion, etc.) when it moves through a magnetic field.

True

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Question

A magnetic field is a region in space where a moving neutrally charged particle feels a force.

False

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Question

What is the name of the force exerted by the magnetic fields on a charge?

Magnetic force or Electromagnetic force. Also known as Lorentz force.

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Question

A charged particle can be stationary in a magnetic field and still feel a magnetic force.

False

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Question

What requisites need to be imposed on a particle for it to be affected by a magnetic field?

It has an electrical charge and it is moving relative to the magnetic field.

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Question

Is a moving charge affected by a magnetic field perpendicular to its velocity?

Yes, the magnetic force is maximized when the movement of the particle is perpendicular to the magnetic field direction.

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Question

True

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Question

What movement does a moving charge describe when affected by a uniform magnetic field?

A circular trajectory.

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Question

Alpha and beta particles are moving with the same speed perpendicularly to a magnetic field. The alpha particles will undergo a deflection that is ... the deflection of the beta particles.

less than

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Question

Alpha particles and beta particles will deflect in opposite directions when entering a uniform magnetic field due to ...

their opposing charges

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Question

Beta particles are heavier than alpha particles.

False

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Question

A charged particle will move in a straight path when it enters a region with only a magnetic field present, with constant velocity.

False

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