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# Magnetism and Electromagnetic Induction

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Have you ever wondered how hard drives can store multiple terabytes of data in a seemingly small metal box? The largest hard drive available for retail purchase is now around 20 Terabytes, which is almost 20,000 movies! The secret behind these enormous storage systems lies in magnetism and electromagnetic induction; this field studies how magnetic fields and electric fields are intrinsically linked to one another. This results in electromagnetic induction, which is the generation of an electromotive force or EMF when an alternating magnetic field interacts with a conductor.

Fig. 1 - Modern commercial hard drives can hold up to 20 Terabytes of data.

Electromagnetism is used to store data on hard drives in a binary format of 1s and 0s. Because magnets have two opposite poles, machines can be used to induce a north or south pole onto a magnetic material to represent either a one or a zero. What's important is that we can represent two distinct states to form a 'bit' which is the smallest unit of information. Therefore, when the data has to be read back, your computer can read these poles and interpret them into binary code! Keep reading this article to learn more about the applications of magnetism and electromagnetic induction in real life.

## Magnetism Definition

You have most likely come across magnetism in your daily lives. When you place two magnets next to one another, you'll have noticed that, if placed in the correct orientation, they experience an attractive or repulsive force on one another. Therefore we can define magnetism as the following.

Magnetism is defined as the attractive and repulsive forces experienced between charged particles and certain types of materials due to the movement of electric charges.

Not all materials exhibit noticeable magnetic effects as magnetic forces heavily depend on a material's internal structure. We can separate materials into three categories concerning magnetism:

1. Diamagnetism - Materials that experience magnetic forces in a magnetic field, generating a field in the opposite direction to the external field.

2. Paramagnetism - Materials that experience magnetic forces in the presence of a magnetic field, generating a field in the same direction as the external field.

3. Ferromagnetism - Materials that remain magnetic when an external magnetic field is applied and then removed.

You may be familiar with a bar magnet, like the one seen in the picture below. These magnets are typically made up of iron or steel, both of which are ferromagnetic materials,

allowing them to retain their magnetic qualities even when they're not subjected to a magnetic field. This allows for fun science experiments both at home and in the lab when learning about the qualities of magnetism! Furthermore, magnets are also used in various industrial applications such as generators, motors, solenoids, and more. The term ferromagnetism stems from the Latin term "ferrum", meaning iron. As steel is an alloy of iron, ferromagnetic describes materials that have the same magnetic properties as iron.

Fig. 2 - A bar magnet made of iron or steel is an example of a ferromagnetic material.

Furthermore, magnetized materials radiate a magnetic field around them, represented in diagrams using field lines. As shown in the figure below, these field lines are directed, which is represented by arrowheads, and always point out of the north pole and towards the corresponding south pole of the magnet. The higher the density of the magnetic field lines in space, the stronger the magnetic field is in that region. Therefore, we can see the strength of the magnetic field is at its largest in the area around the poles.

We can also define another quantity that is commonly used to describe electromagnetic fields - the magnetic flux.

The magnetic flux passing through a surface is equal to the magnitude of the normal component of that magnetic field strength passing through that surface multiplied by the area of that surface.

This can be represented in the equation

$\Phi = BA \cos(\theta) ,$

where $$\Phi$$ is the magnetic flux measured in Webers $$\mathrm{Wb}$$, $$B$$ is the strength of the magnetic field measured in teslas $$\mathrm{T}$$, $$A$$ is the area in which the magnetic field is passing through measured in $$\mathrm{m^2}$$, and $$\theta$$ is the angle between the magnetic field lines and the area it is passing through. As can be seen from the equation, we are only considering the component of the magnetic field perpendicular to the area it passes through.

## Electromagnetic Induction Definition

On the other hand, we instead define it as the following.

Electromagnetic Induction is defined as the induction of an electromotive force, or current, due to an alternating magnetic field coinciding with a conductive material.

Here, an electromotive force is similar to the potential difference across a circuit, however, it is used to describe voltage when there is no current flowing in a circuit. When we discuss an electromotive force, we refer to the induced voltage due to the induction.

In order to quantify the amount of electromotive force being induced in the conductor, we represent this as an equation

$\epsilon = - \frac{\Delta \Phi_{\text{B}}}{\Delta t} ,$

where $$\epsilon$$ is the induced electromotive force measured in volts $$\mathrm{V}$$, $$\Delta \Phi_{\text{B}}$$ is the change in magnetic flux measured in Webers $$\mathrm{Wb}$$, and $$\Delta t$$ is the time taken for the change measured in seconds $$\mathrm{s}$$. This equation reveals a number of things; firstly, it is the combination of Faraday's law and Lenz's law, which are defined as follows.

Faraday's law states that the amount of induced electromotive force (EMF) is proportional to the rate of change of magnetic flux.

And Lenz's law is as follows.

Lenz's law states the direction of the induced current is such that it opposes the change causing it.

These two laws govern the phenomenon of electromagnetic induction. Let us first talk about Faraday's law; we can see from the equation above that the proportionality constant is given by $$N$$, the number of turns in the solenoid. We can see that this equation is specifically for a solenoid undergoing induction, but it may vary depending on the type of conductor we are looking at.

On the other hand, Lenz's law is represented in the equation as the negative sign on the right-hand side, showcasing that the direction of the electromotive force must be opposite to that of the rate of change of magnetic flux. This law stems from energy conservation, which states that energy cannot be created or destroyed. In order to further understand this, consider a bar magnet falling through a coil of wire; the induced current in the wire causes a magnetic field surrounding it. This field interacts with the falling magnet, exerting a force on it. As a result of Lenz's law, the direction of the force must be such that it opposes the motion of the magnet, ie. in the upwards direction. This causes the magnet to slow down and reduce the amount of induced current in the coil. Otherwise, a downwards force causing the magnet to speed up would result in a larger current being induced in the coil, an endless loop of energy being created which isn't allowed in physics!

## Difference between Magnetic Induction and Electromagnetic Induction

You may have already heard of magnetic induction before you came across this article, and are asking yourself - is magnetic and electromagnetic induction the same thing? These two phenomena are actually very different things, so let us first define what magnetic induction is.

Magnetic induction is defined as the magnetization of magnetic materials, such as ferromagnetic or paramagnetic, under the influence of an external magnetic field.

As we mentioned in the previous section, we established that all materials can be categorized into three magnetic categories. In order for these materials to be magnetized by an external magnetic field, they must either be ferromagnetic or paramagnetic. To understand the structure of magnetic materials, we zoom into the internal structure of the substance and look at its building blocks, the atoms. These individual atoms reside in magnetic domains where the atom itself becomes a magnetic dipole.

A magnetic dipole is a structure consisting of a magnetic north pole and a magnetic south pole.

Essentially, we can think of magnetic materials as being made up of many individual bar magnets! These bar magnets are susceptible to the influence of an external magnetic field, rotating back and forth depending on the orientation of the field. Let's look at the figure below to get a clearer picture of the structure.

Fig. 4 - Magnetic materials are made up of individual magnetic dipoles. Here the material is unmagnetized as all of the dipoles are in different orientations.

In the figure above, we have the magnetic material outlined in blue, whilst the magnetic dipoles are represented by the pink arrows. In this case, the direction of the arrows indicates the north magnetic pole. Here we can see that all of the arrows are pointing in different directions, showing that the dipoles are not under a magnetic field to organize their orientations. Thus we know that this material is not magnetized.

Fig. 5 - The magnetic dipoles are aligned, showing that the material now exhibits magnetic properties due to its net magnetization.

Now in the figure above, we have the same material except that the magnetic dipoles are all orientated in the same direction. In this case, an external magnetic field has been applied to the material, causing the dipoles to rotate. The resultant alignment of the magnetic fields is what causes the magnetic properties within the material.

Therefore, now we have a clear distinction between magnetic induction, which is the process of magnetizing materials, and electromagnetic induction, which is the procedure of generating an electromotive force in a conductor. Two phenomena with very similar names but very different outcomes!

## Example of Magnetism

In order to further understand magnetism, let's consider a numerical example of how to calculate the magnetic flux.

Consider a magnetic field of strength $$2.5\,\mathrm{mT}$$ passing through a square area with side length $$15\,\mathrm{cm}$$. If the field lines are at an angle of $$30^{\circ}$$ to the normal of the surface, what is the magnetic flux of the field passing through?

Firstly, we calculate the area of the surface. As the surface is a square shape, we find that

$A = 15 \times 10^{-2} \, \mathrm{m} \times 15 \times 10^{-2} \,\mathrm{m} = 0.023\,\mathrm{m^2}.$

Finally, we can substitute all our remaining numbers into our equation for magnetic flux, $\Phi = BA \cos(\theta) ,$ to find

$\Phi_{\text{B}} = 2.5\times 10^{-3} \, \mathrm{T} \times 0.023\,\mathrm{m^2} \times \cos(30^{\circ}) = 5.0\times 10^{-5}\,\mathrm{Wb},$

where we have used the fact that $$1 \, \mathrm{T} = 1 \, \mathrm{\frac{kg}{s^2 \, A}}$$ and $$1 \, \mathrm{Wb} = 1 \, \mathrm{\frac{ kg \, m^2}{s^2 \, A}}$$.

Now let's consider another example where we apply our electromagnetic induction equation instead.

Consider an electromagnet rotating next to a solenoid coil connected to a voltmeter. The rotation of the solenoid creates a change in the magnetic flux of $$2.1 \, \mathrm{m Wb}$$ in a time of $$1.5 \, \mathrm{s}$$. What would be the average reading on the voltmeter due to the resultant electromagnetic induction?

Using our electromagnetic induction equation, we can substitute the numbers above to give

\begin{align} \epsilon &= \frac{\Delta \Phi_{\text{B}}}{\Delta t} \\ \epsilon &= \frac{ 2.1 \times 10^{-3} \, \mathrm{Wb}}{ 1.5 \, \mathrm{s}} \\ \epsilon &= 1.4 \times 10^{-3} \, \mathrm{V} . \end{align}

## Electromagnetic Induction Real Life Applications

As we mentioned earlier in the article, electromagnetic induction is a key component of many objects we use in day-to-day life. One that you may have come across recently is commonly found in the kitchen and is essential to making your food daily. Can you guess what it is?

Fig. 6 - An induction hob is an example of electromagnetic induction being used in objects we use in our everyday lives.

That's right! It's an induction hob. An induction hob is a great example of how electromagnetic induction has allowed technology to be improved and developed with added safety benefits. In the case of the induction hob, the inside of the heating element consists of coils made up of conducting material, with an alternating current running through them. The alternating current generates an oscillating magnetic field on the surface where you place your frying pan. You may have noticed that only specific types of pans work with induction cookers; this is because the pan must be made of a conducting material such that the changing magnetic field can induce a current in the bottom of the pan. Due to the internal resistance of the pan, the currents running through the pan generate heat which is then used to make your morning breakfast!

Fig. 7 - Graphic tablets also use electromagnetic induction to detect inputs from the user.

Another example of electromagnetic induction being used in real-life applications is the graphics tablet. This device is typically used by artists who want to create digital art without losing the pen-on-paper experience. As the pen is moved across the surface of the tablet, the tip of the graphics pen exudes an electromagnetic field which then interacts with the conductors beneath the surface of the tablet. Through electromagnetic induction, the computer can process those induced signals into the lines being drawn by the artists, resulting in the image you see on the screen!

## Magnetism and Electromagnetic Induction - Key takeaways

• Magnetism is defined as the attractive and repulsive forces experienced between magnetic materials due to the movement of electric charges.
• Materials can be sorted into three categories: ferromagnetic, diamagnetic, and paramagnetic.
• The magnetic flux is defined as the amount of magnetic field passing through a certain area and is given by the equation $$\Phi = BA \cos(\theta)$$.
• Electromagnetic induction is defined as the induction of an electromotive force, or current, due to an alternating magnetic field coinciding with a conductive material, and is given by the equation $$\epsilon = -N\frac{\Delta \Phi}{\Delta t}$$.
• Electromagnetic induction is governed by Faraday's law and Lenz's law.

## References

1. Fig. 1 - Hard drive, flickr.com (https://flickr.com/photos/philipus/29711988683/in/photolist-MgxH5X-2mWucxQ-3mKAy8-8hahaE-2mJm7HY-2kHTYVX-2m4Z1az-2mUN4XJ-2nhVpo6-2mjsY3V-2mjwPed-2mjBQxE-2mjybYf-SyQdMo-2mjAGRZ-JJg4p6-2mXZLK5-2iyEqss-2j2riAF-Lgoj1U-2gcE71E-2iyEqpM-227cN6x-pRMmju-663UrM-2nkMGxP-EdqoHi-2mjBQd6-22GRnAQ-2mXZLja-2mjycJi-23hg9kX-2kLX2wo-2kHAKwa-ggGpw-24mwD2D-JBJELX-e8zs1D-oTAM7A-oWQ7LY-2cX8gg7-22QFeqe-6y1CMR-8VkTe-23hgGvt-Ecsgfu-7yY3rX-zMew7V-2jjueQr-4C1jRz) Licensed by CC BY-NC-ND 2.0 (https://creativecommons.org/licenses/by-nc-nd/2.0/)
2. Fig. 2 - Bar magnet, Wikimedia Commons (https://commons.wikimedia.org/wiki/File:Bar_magnet_crop.jpg) Licensed by CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0/)
3. Fig. 3 - Magnetic field lines, StudySmarter Originals.
4. Fig. 4 - Unaligned atomic dipoles, StudySmarter Originals.
5. Fig. 5 - Aligned atomic dipoles, StudySmarter Originals.
6. Fig. 6 - Induction Hob, Wikimedia Commons (https://commons.wikimedia.org/wiki/File:Kookplaat_inductie.JPG) Licensed by CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0/)
7. Fig. 7 - Graphics tablet, Wikimedia Commons (https://commons.wikimedia.org/wiki/File:Wacom_Pen-tablet_without_mouse.jpg) Licensed by CC BY-SA 2.5 (https://creativecommons.org/licenses/by-sa/2.5/)

Electromagnetic induction works due to an alternating magnetic field interacting with a conductor, inducing an electromotive force in the conductor.

The induced electromotive force generates a current in the conductor. This in turn results in electricity running through the conductor.

Magnetic induction is the process of magnetizing materials by aligning the magnetic domains inside the material.

This induces an electromotive force in the conductor.

This is when a voltage is conducted in a conductor due to the presence of a changing magnetic field.

## Final Magnetism and Electromagnetic Induction Quiz

Question

What is the definition of Faraday's law?

Faraday's law states that the induced electromotive force is proportional to the rate of change of magnetic flux in the field.

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Question

What is the definition of Lenz's law?

Lenz's law states that the direction of the induced current is to oppose the motion causing it.

Show question

Question

What is the mathematical expression for electromagnetic induction?

$$\epsilon = -\frac{\Delta \Phi_{B}}{\Delta t}$$.

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Question

How do we define magnetic flux?

Magnetic flux is the perpendicular component of a magnetic field passing through an area.

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Question

What is the mathematical expression for magnetic flux?

$$\Phi = |\vec{B}| \cos(\theta) |\vec{A}|$$.

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Question

How do the magnetic field lines travel between the poles of a magnet?

From North to South.

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Question

When a stationary magnet is placed next to a coil, an electromotive force is induced in the coil.

False.

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Question

When a falling magnet is dropped next to a wire, an electromotive is induced in the wire.

True.

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Question

A moving coil passes by a stationary magnet, inducing an electromotive in the coil.

True.

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Question

A transformer can only be used to change larger voltages to smaller voltages.

False.

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Question

Magnetic field lines from a magnet are at $$30^{\circ}$$ to a square area of length $$6.0\,\mathrm{cm}$$. If the magnetic field strength has a value of $$0.01\,\mathrm{T}$$, what is the magnetic flux?

$$3.1\times 10^{-5}\,\mathrm{Wb}$$.

Show question

Question

How much electromotive force is induced in a coil of $$N=10$$ turns by a change of magnetic flux of $$1.5\,\mathrm{mWb}$$ in $$30\,\mathrm{s}$$?

$$-5.0\times 10^{-4}\,\mathrm{V}$$.

Show question

Question

For a transformer with $$N_{\text{in}} = 10$$, $$N_{\text{out}} = 20$$, and $$V_{\text{out}} = 80\,\mathrm{V}$$, what is the input voltage?

$$40\,\mathrm{V}$$.

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Question

Magnetic field lines from a magnet are at $$70^{\circ}$$ to a circular area of radius $$2\,\mathrm{cm}$$. If the magnetic field has a value of $$0.02\,\mathrm{T}$$, what is the magnetic flux?

$$8.6\times 10^{-6}\,\mathrm{Wb}$$.

Show question

Question

For a transformer with $$N_{\text{in}} = 45$$, $$N_{\text{out}} = 10$$, and $$V_{\text{in}} = 40\,\mathrm{V}$$, what is the output voltage?

$$8.9\,\mathrm{V}$$.

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Question

What is the definition of Lenz's law?

The direction of an induced current will always be in the direction to oppose the motion causing it.

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Question

How do we hold our right hand to use the right-hand grip rule?

Thumb points up, fingers curled.

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Question

In which direction does our thumb point in the right-hand grip rule?

North pole.

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Question

In which direction do our fingers point in the right-hand grip rule?

In the direction of the current.

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Question

What is the equation for electromagnetic induction in a conductor?

$$\epsilon = - \frac{\Delta \Phi_{\text{B}}}{\Delta t}$$.

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Question

When a magnet falls through a tube made up of conducting material, what happens to its motion?

The induced current in the tube generates an opposing force to the magnet, slowing its motion.

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Question

There are two copper coils, one with $$N_1 = 6$$ turns and the other with $$N_2 = 10$$ turns. If a magnet is dropped through both of the coils at the same rate, which coil has a larger magnitude of EMF induced?

The coil with $$N_2 = 10$$ turns.

Show question

Question

As a magnet passes by a wire, the change in electromagnetic flux is given by $$6.5\,\mathrm{mWb}$$ in $$2.5\,\mathrm{s}$$. What is the magnitude of the induced electromotive force?

$$2.6\,\mathrm{mV}$$.

Show question

Question

As a magnet passes by a wire, the change in electromagnetic flux is given by $$6.5\,\mathrm{mWb}$$ in $$2.5\,\mathrm{s}$$. If the resistance of the wire in is given by $$R=60\,\mathrm{\Omega}$$, what is the induced current?

$$-4.3\times 10^{-5}\,\mathrm{A}$$.

Show question

Question

As a magnet passes by a coil, the change in electromagnetic flux is given by $$12 \times 10^{-2}\,\mathrm{Wb}$$ in $$5.0\,\mathrm{s}$$. What is the induced electromotive force?

$$-2.4\,\mathrm{mV}$$.

Show question

Question

As a magnet passes by a coil, the change in electromagnetic flux is given by $$12 \times 10^{-2}\,\mathrm{Wb}$$ in $$5.0\,\mathrm{s}$$. If the resistance of the coil is given by $$R=100\,\mathrm{\Omega}$$, what is the induced current?

$$-2.4\times 10^{-5}\,\mathrm{A}$$.

Show question

Question

As a magnet passes by a wire, the change in electromagnetic flux is given by $$8.0\,\mathrm{mWb}$$ in $$1.0\,\mathrm{s}$$. What is the induced EMF?

$$-8.0\,\mathrm{mV}$$.

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Question

If a current traveling through a wire is pointing directly out of the page, what is the orientation of the magnetic field?

Anticlockwise.

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Question

What is the name of the force due to the interaction between a charged particle and an electromagnetic field?

Lorentz force.

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Question

What is the equation for the Lorentz force?

$$\vec{F} = q\vec{v}\times \vec{B}$$.

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Question

How do we calculate the magnitude of a cross product?

$$| \vec{a} \times \vec{b}| = |a|\, |b| \sin(\theta)$$.

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Question

How do we calculate the magnitude of the Lorentz force?

$$|F| = qvB\sin(\theta)$$.

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Question

How do you orient your hands to use the right-hand rule?

Thumb, fingers and palm point in orthogonal directions to one another.

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Question

In the right-hand rule, what does the thumb point in the direction of?

The velocity of the particle.

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Question

In the right-hand rule, what do the fingers point in the direction of?

The field.

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Question

In the right-hand rule, what does the palm point in the direction of?

The force.

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Question

When the particles are negatively charged, which direction do we point our thumb in for the right-hand rule?

Opposite to the flow of negatively charged particles.

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Question

What direction is the Lorentz force with respect to the trajectory of the charged particles?

Perpendicular to the flow of charged particles.

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Question

What other force can we equate the Lorentz force to?

Centripetal force.

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Question

What is the equation for the velocity $$v$$ of a charged particle in an electromagnetic field?

$$v = \frac{Bqr\sin(\theta)}{m}$$.

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Question

When representing the magnetic field, what does the cross symbol represent?

Field going into the page.

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Question

When representing the magnetic field, what does the circle symbol represent?

Field coming out of the page.

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Question

What is the magnitude of the Lorentz force for an electron traveling through a perpendicular magnetic field of strength $$B = 2.5\,\mathrm{mT}$$ with a velocity $$v = 7.5\,\mathrm{\frac{m}{s}}$$?

$$3.0\times 10^{-21}\,\mathrm{N}$$.

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Question

What is the expression for the magnetic field generated by a current-carrying wire?

$$B = \frac{\mu_{0}}{2\pi}\frac{I}{r}$$.

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Question

What is the shape of the magnetic field generated by a current-carrying wire?

Concentric circles.

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Question

How does the strength of the magnetic field vary with radial distance $$r$$ from the wire?

Inversely.

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Question

How does the strength of the magnetic field vary with current $$I$$ in the wire?

Proportionally.

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Question

How do we determine the direction of the magnetic field from a current-carrying wire?

Right-hand grip rule.

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Question

In what direction does the thumb point in the right-hand grip rule?

Current.

Show question

Question

In what direction do the curled fingers point in the right-hand grip rule?

Magnetic field.

Show question

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