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Magnetic Fields

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Magnetic Fields

A magnetic field is a part of space where a force is applied at every point. That force comes from a source that can be of various nature. In the case of a magnetic fields, it is either electrical or magnetic.

Magnetic Field Lines

When you put a magnet under a thin surface and throw metal shards on top, a shape similar to the one in Figure 1 will appear. The reason for this is that, like the needle of a compass, every shard aligns with the lines of the magnetic field generated by the magnet. Those lines represent the force vectors of the field. The denser they are in a region of space, the stronger the field in that region is.

Magnetic Fields, Magnetic Field pattern around a bar magnet, StudySmarterLines created by a magnet applied to iron particles

You should note that every line is a closed loop going from one pole to the other, and this is the quality that makes a field solenoidal. This differs from the electric field because of the absence of the magnetic monopole and is strictly connected to it because the magnetic and electric fields generate each other through the movement of the charges. To understand the relationship between these two fields, we must consider the Lorentz force.

The Direction of Magnetic Field: The Lorentz force

Consider an electric field, a magnetic field, and an electrically charged particle passing through them. That particle will be subject to a force that is dependent upon both fields and perpendicular to the magnetic field. These three physical quantities together always constitute an ordered triplet like the cartesian axis. To visualize this relationship, you can use Fleming's rule of the left hand. Going counterclockwise, you have two vectors and their vector product, respectively.

Fleming's left-hand rule tells us the direction of the vectorial product with respect to the direction of the vectors. The Lorentz force F has the direction of the vectorial product between the velocity v and the magnetic field B.

Magnetic Fields, Fleming's left hand rule, StudySmarterFleming's left hand rule, Camacho - StudySmarter Originals

The expression for the Lorentz force is:

Here q is the charge, E is the electric field, v is the speed of the particle, and B is the magnetic field.

Applying it to the Lorentz force, this has the direction of the thumb when the velocity is along the middle finger, and the magnetic field is parallel to the index finger. There is a also useful rule called the right hand rule to see the magnetic field of a live wire by pointing the thumb in the direction of the current, while the other fingers grabbing the wire represent the magnetic field.

Magnetic Fields: What is the difference between H and B?

When considering the vacuum as the area where the field is present, it is roughly the same to consider the magnetic field strength or the magnetic field flux density because these quantities are proportional. But within a material, we can observe the difference between them. The flux is the portion of the field passing through a surface every second.

Magnetic flux density

The term magnetic field is used to describe two different (but deeply related) quantities. H is the magnetic field's intensity and B is the magnetic flux density These quantities in the vacuum are proportional because of vacuum permeability.

Instead, within a material, the magnetization M is subtracted from the term calculating the field B. This is also called magnetic flux density :

Magnetization takes into account the effect of the magnetic polarization in the material, a concept that is dual to the electric polarization and gives symmetry to the formulas describing the electromagnetic field.

What is electromagnetic induction?

Electric fields and magnetic fields generate each other, but how does that happen? The explanation is electromagnetic induction, which is the phenomenon causing a current to be generated into a conductor thanks to a magnetic field.

Generating an electromotive force with a magnetic field (Faraday's law)

Lenz's law states that the (induced) magnetic field generated by the induction current within a material by an external magnetic field opposes this last one. This makes perfect sense as, otherwise, the magnetic field within the material will increase exponentially.

Faraday studied the effect of a magnetic field applied to an electric circuit and discovered that moving a magnet with the circuit immersed into its field, or moving a magnet into a loop formed by the circuit, causes a current to flow in the circuit itself. Moreover, this current is proportional to the speed of the movement that is represented by the time derivative d / dt of the magnetic field flux ΦB:

EMF here is the electromotive force measured in Volts.

Magnetic Fields: Alternating current

An invention that works on the principle of induction and uses the magnetic field to generate a current is the induction motor that produces an AC current. It consists of a magnetically charged armature called a stator, which contains a moving part called a rotor. The rotor is connected to the circuit through wirings that sense the magnetic field, which always faces the same direction but imposes a current that changes as the rotor moves.

An alternating current is created, which has a sinusoidal waveform and is expressed in the form:

Magnetic Fields, Copper coil producing current, StudySmarterThe movement of a copper coil (in copper color) inside a magnet (left) produces a current flow that alternates in time (right).

It should be noted that by inverting the functions of the stator and the rotor in a magnetic field generating a current, you obtain a circuit that generates mechanical movement.

Magnetic Fields: Inductance and flux linkage

Loops interact with the magnetic field. Thus, the element that inherits this quality into an electrical circuit is the inductor. To study how it works, let us make some definitions. The flux linkage , which is mainly used in engineering applications, is defined as the total flux passing through a coil. This is obtained by multiplying the magnetic flux by the number N of loops:

The inductance, identified by the letter L, is defined as the magnetic linkage of an object divided by the current that causes that flux:

When the current causing the flux linkage is also the one linking the coil (there are no currents external to the coil), this equation becomes simpler, as there is no more need for subscripts. It then takes the name of self-inductance.

Imagine you have a coil with 500 turns, through which passes a current of 10A that generates a magnetic field of 10mWb. In 10ms, what will be the EMF generated?

Using both formulas: L = 500 ⋅ 0.01Wb / 10A = 0.5H

So, EMF = 0.5H ⋅ 10A / 0.01s = 500V

Magnetic Fields (A2 Only) - Key takeaways

  • The magnetic field is strictly linked to the electrical field. The two generate each other and are the two faces of the same medal: the electromagnetic force.
  • There is a difference between H and B when the field is applied to a material while they have the same value in a vacuum.
  • When an electromagnetic field is applied to a moving particle, particle is subject to a perpendicular force called the Lorentz force.
  • The phenomenon of induction causes a magnetic field to be generated by an electric field.
  • Remarkable inventions based on induction are the AC motor or induction motor and the transformer.

Frequently Asked Questions about Magnetic Fields

 It is the area where the magnetic force acts on particles.

The magnetic field is the strongest at the poles because of the concentration of field lines.

Earth has a magnetic field because there are currents flowing in its core.


Mars doesn't have a magnetic field, even though it used to.


The magnetic field is measured in [A] / [m]

Final Magnetic Fields Quiz

Question

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

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Electric charges are measured in Coulombs.

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The vector product is an operation between two vectors that yields a vector perpendicular to the other two.

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A moving charged particle in a uniform magnetic field describes a circular trajectory.

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Cyclotrons and synchrotrons use electric fields to linearly accelerate particles and a magnetic field to curve their trajectory.

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

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Lorentz force.

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What is the name of the rule that helps to determine the direction of the vector obtained by a vector product?

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Right-hand rule.

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Is the order of the vector product irrelevant?

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No, changing the order yields a global minus sign.

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

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It must have a charge, and it must be moving.

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

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Yes, the Lorentz force is maximised in this case.

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Does a uniform magnetic field change the energy of a moving charge?

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No, since it does not change its speed.

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

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A circular trajectory.

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How does one manage to initially accelerate a charge in a cyclotron?

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With the help of an electric field.

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How does one manage to periodically accelerate a charge in a cyclotron?

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By increasing the value of the magnetic field.

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Are there any relativistic effects in cyclotrons when approaching speeds close to the speed of light?

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Yes, there are, and it is this that caused the development of synchrotrons.

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Electric fields and magnetic fields are two sides of the same coin: the electromagnetic field.

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Electric currents are the basic objects generating and being affected by magnetic fields.

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The magnetic flux density created by a wire is directed twisting around the wire.

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The magnetic flux density created by a wire increases as the current flowing through the wire increases.

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The magnetic flux density is a measure of the strength of the magnetic field per unit of length and current.

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What is an electric current?

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It is the effect caused by electric charges in movement.

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What are the laws that describe electromagnetism?

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Maxwell’s laws.

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As a physical system, it does not matter whether an electric charge is moving or static. True or false?

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False.

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Does the magnetic field generate a force in the direction it is defined?

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No, it generates a force in a direction perpendicular to it.

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Are currents affected by magnetic fields?

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Yes, they are.

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Is the magnetic force on a wire carrying a current dependent on the length of the wire?

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Yes, and on the current carried by the wire.

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What is the direction of the magnetic field created by a wire?

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It is directed in the direction where it forms circles around the wire.

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Does the magnetic field created by a wire decrease with radial distance (inverse relationship)?

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Yes, it does.

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Do two parallel wires with current exert a force on each other?

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Yes, they do.

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Do two perpendicular wires with current exert a force on each other?

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No, they generate fields parallel to the other wire’s current.

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The magnetic field is a vector field.

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The magnetic flux is a quantity that measures the amount of magnetic field crossing a certain surface.

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Faraday's law states that an electromotive force appears when the magnetic flux changes over time.

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Magnetic flux linkage refers to an experimental setup where several coils are used to increase the net flux.

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The magnetic flux is zero when the magnetic field is parallel to the surface.

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What is the magnetic flux?

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It is a quantity measuring the amount of magnetic field crossing a certain surface.

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What are the three basic variable elements in the expression for the magnetic flux?

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Strength of magnetic field, area of the surface and relative orientation.

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Can the magnetic flux be calculated only for flat surfaces?

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No.

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What is the usual experimental setup for generating an oscillating electromotive force?

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A rotating coil.

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What is the usual varying quantity in the magnetic flux when considering several coils?

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The strength of the magnetic field.

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In which units is the magnetic field measured?

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Teslas.

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In which unit is the magnetic flux measured?

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In Webers.

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Are the units of the magnetic flux different from the magnetic flux linkage?

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No, they are the same.

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What is one way to increase the output values of an experimental setup with one coil and a magnetic field?

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Answer

Increase the number of coils.

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Is Faraday's law a Maxwell law?

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Yes.

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Are electric and magnetic fields related to each other?

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Yes, they are.

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Question

There is a sheet with a magnet below. What happens when you throw iron blisters on top of the sheet?


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They will align with the magnetic field of the magnet.

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Why do blisters around a magnet always align in the same way?


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The reason for this is that they align themselves to the direction of the magnetic field.

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What is an ordered triplet?


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An ordered triplet is made by two vectors and their vector product.

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What is the Lorentz force?


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It is the force to which a particle is subject when moving into an electromagnetic field.

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