Fiveable
Fiveable

or

Log in

Find what you need to study


Light

Find what you need to study

5.5 Magnetic Fields and Forces

7 min readdecember 31, 2022

Peter Apps

Peter Apps

Daniella Garcia-Loos

Daniella Garcia-Loos

Peter Apps

Peter Apps

Daniella Garcia-Loos

Daniella Garcia-Loos

Magnetic Fields

What Makes Something a Magnet?

If you look around, most of the objects you encounter in your daily life aren't magnetic. This shouldn't be a surprise though, because creating a magnet requires a very specific set of both micro and macroscopic features. To begin with, we've known since the 1920's that a moving charged object can create a and become its own tiny magnet. For reasons that we won't get into here, it's primarily the electrons that determine the overall of the atom. These electrons can cause natural magnets to occur in elements with half-filled energy levels.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-4RztVdKCpRyr.png?alt=media&token=b636a48a-2070-4f4a-b7cd-1aed9da6eaa2

Image Courtesy of Minute Physics

Collections of these elements can create that can align (or be forced to align) to create an overall . In the image below we can see an external (yellow arrows) can be used to force the individual into alignment which magnetizes the entire material. This is similar to how when a magnet picks up a paperclip, the paperclip becomes magnetized.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-2IOoKtvHRMgt.png?alt=media&token=541e99f3-afe2-4f5a-a499-41477aa6bf8d

Image Courtesy of Wikipedia

Check out this video by Minute Physics for a great overview of this.

What Does a Magnetic Field Look Like?

You may remember playing with magnets in elementary school, using a compass or iron filings to show the shape of the field. lines show the direction that the north pole of a magnet will be pushed or pulled. Just like electric charges, we can use the rule "likes repel, opposites attract". So, a north pole will repel other north poles and be attracted to south poles. Also, like electric fields, we can tell the strength of the field visually by looking at how close the lines are together.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-ubzK0ibyeyiR.gif?alt=media&token=06456cdb-1f77-440c-940a-3955888b3362

Image Courtesy of stickmanphysics

Here are some key points about how a magnetic dipole can be created:

  • A magnetic dipole is a that has two poles (north and south) and behaves like a tiny magnet.
  • A magnetic dipole can be created by separating the north and south poles of a magnet.
  • A magnetic dipole can also be created by placing a current-carrying wire in a . The will cause the charges in the wire to move, creating a north pole at one end of the wire and a south pole at the other end.
  • A magnetic dipole can be represented by a magnetic moment vector, which points from the south pole to the north pole and has a magnitude equal to the product of the pole strength and the distance between the poles.
  • The strength of a magnetic dipole decreases as the distance between the poles increases.
  • Magnetic dipoles can be used to model the magnetic fields of small magnets and current-carrying wires.

The Earth also produces a that protects us from a variety of . The charged particles from the spiral along the lines and collect around the poles resulting in . In order for this to occur, particles need to be charged to be affected by the Earth's .

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-a32WV943fXQj.jpeg?alt=media&token=ed8e90fe-94e1-45dd-814c-4ebf8b9fa3d9

Image Courtesy of wikipedia

strength is represented by B and has units of Tesla (T) where 1T = Ns / Cm. (Aren't you happy we can just write Tesla instead of Newton second per Coulomb meter? I am! 😄)

Magnetic Force from a Moving Charged Particle

So, why do charged particles curve in a ? They experience a force! The force from a can be calculated using this equation:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-ozwM6ecYC6uU.png?alt=media&token=cf98653e-6c96-4a61-ad97-e7a80a708dfa

Looking at this equation, we can see that in order to be affected by a magnetic force:

  1. The object must be charged (q ≠ 0)

  2. The particle must be moving (v ≠ 0)

  3. There must be a (B ≠ 0)

  4. The particle and the field must have a perpendicular component (cross product)

Ok, so we can calculate the magnitude of the force, but what about its direction? This can be easily found using the Right-Hand Rule (RHR). Point your thumb in the direction a positive charge is moving, your other fingers in the direction of the , and your palm will face the direction of the force.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-CYIehMJexrdi.jpg?alt=media&token=358ef731-c9db-4f03-88c9-c6a239444058

Image Courtesy of schoolbag.info

Magnetic Force from a Current in a Wire

So we've seen that a charge moving through a experiences a magnetic force. Let's apply the same concept to a wire and see what happens.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-ojwUGsM6qhSX.jpg?alt=media&token=dd7f88a4-8979-4657-ae0a-8909101476c0

Image Courtesy of cnx

Any wire with current passing through it becomes an electromagnet. The lines are circular around the wire radiating outwards. Again, we can use the right-hand rule to determine the direction of the . This application will be referred to as the Right-Hand Curl Rule (RHCR) since we now have 2 applications of this rule.

To do the RHCR, you position your hand with your thumb pointing in the direction of the current and curl your fingers around the wire. Your fingers point in the direction of the . In the example above, the $B$ field is coming out of the page to the left of the wire and going into the page on the right side of the wire.

The internal created by a very long current-carrying wire can be determined using the equation:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-CPz0MA8gRaYE.png?alt=media&token=43b2b501-1010-4962-841e-899ef542453c

I is the current flowing through the wire, μo is the permeability of free space constant (found on the front page of your reference tables), and r is the distance away from the wire.

For a more detailed explanation of how this phenomenon works, check out part 2 of the Minute Physics video series on magnets.

Here are some key things to remember when drawing a :

  • A is a region around a magnet or electric current where the force of magnetism can be detected.
  • The direction of the at a particular point is the direction that a north pole of a magnet would point if it were placed at that point.
  • The strength of the at a particular point is related to the density of the field lines at that point. Field lines that are closer together indicate a stronger .
  • The lines around a magnet form closed loops, with the direction of the field given by the right-hand rule.
  • The lines around a current-carrying wire form concentric circles around the wire, with the direction of the field given by the right-hand rule.
  • When drawing a , it is important to pay attention to the direction of the field lines and the strength of the field at different points.
  • You can use a viewer (such as iron filings or a piece of paper with a magnet placed under it) to visualize the shape and direction of the .

Practice Questions

1.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-BA0dgvBrJmQZ.png?alt=media&token=26a71b44-7a41-42a7-a945-c73da74d4285

Image Courtesy of the AP Physics 2 Course & Exam Description

Answer

Choice B is correct. Use the Right Hand Rule twice. First to find the direction of the around the wire (should be coming out of the page above the wire, and into the page below the wire) then again to find the direction of the force the wire exerts on the charge (should be towards the the bottom of the page). The question asks for the force the charge exerts on the wire which is a Newton's 3rd Law pair with the force we just found. So the wire pushes the charge towards the bottom of the page and the charge pushes the wire towards the top of the page.

2. A negatively charged particle is moving with a speed of vo when it enters a region with B directed into the page. The dark curve shows the path the particle moved in the field.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-ee1rP7Can0XP.png?alt=media&token=ddffa0a8-0241-4878-a4e5-dddff5f1fad9

What, if anything, is wrong with this diagram?

Answer

There are 2 major problems with this diagram

  • The particle should curve downwards not upwards in this field. The Right Hand Rule gives us a upwards force for a positive particle so the negative charge must experience a force downwards and therefore curve down towards the bottom of the page

  • The magnetic force is always perpendicular to the velocity of the particle, so the particle will always move in and move in an arc (1/4 of a circle) instead of the curve shown above.

Key Terms to Review (10)

Auroras

: Auroras are natural light displays that occur in the Earth's atmosphere, primarily near the polar regions. They are caused by interactions between charged particles from the sun (solar wind) and atoms or molecules in Earth's upper atmosphere.

Cosmic radiation

: Cosmic radiation refers to high-energy particles that originate from outside of Earth's atmosphere, such as protons and atomic nuclei. These particles can come from various sources in space, including the sun, distant stars, and even black holes.

Electron

: Electrons are subatomic particles that have a negative charge and orbit around the nucleus of an atom. They play a crucial role in determining the chemical properties and behavior of elements.

Magnetic domains

: Magnetic domains are small regions within ferromagnetic materials where groups of atoms align their magnetic fields in the same direction. These aligned domains contribute to the overall magnetization of the material.

Magnetic field

: A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges or by magnets.

Permeability of free space (μo)

: Permeability of free space refers to the measure of how easily a magnetic field can pass through a vacuum. It is a fundamental constant in physics that determines the strength and behavior of magnetic fields.

Right-Hand Rule (RHR)

: The Right-Hand Rule is a method used to determine the direction of magnetic fields, magnetic forces, and induced currents in wires.

Solar wind

: Solar wind refers to a continuous flow of charged particles (mainly electrons and protons) emitted by the sun into space. This stream of particles carries energy and magnetic fields throughout the solar system.

Tesla (T)

: Tesla is the unit used to measure the strength of a magnetic field. One tesla is equal to one newton per ampere-meter.

Uniform circular motion

: Uniform circular motion refers to the movement of an object in a circle at a constant speed, where its velocity is always changing due to its direction constantly changing.

5.5 Magnetic Fields and Forces

7 min readdecember 31, 2022

Peter Apps

Peter Apps

Daniella Garcia-Loos

Daniella Garcia-Loos

Peter Apps

Peter Apps

Daniella Garcia-Loos

Daniella Garcia-Loos

Magnetic Fields

What Makes Something a Magnet?

If you look around, most of the objects you encounter in your daily life aren't magnetic. This shouldn't be a surprise though, because creating a magnet requires a very specific set of both micro and macroscopic features. To begin with, we've known since the 1920's that a moving charged object can create a and become its own tiny magnet. For reasons that we won't get into here, it's primarily the electrons that determine the overall of the atom. These electrons can cause natural magnets to occur in elements with half-filled energy levels.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-4RztVdKCpRyr.png?alt=media&token=b636a48a-2070-4f4a-b7cd-1aed9da6eaa2

Image Courtesy of Minute Physics

Collections of these elements can create that can align (or be forced to align) to create an overall . In the image below we can see an external (yellow arrows) can be used to force the individual into alignment which magnetizes the entire material. This is similar to how when a magnet picks up a paperclip, the paperclip becomes magnetized.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-2IOoKtvHRMgt.png?alt=media&token=541e99f3-afe2-4f5a-a499-41477aa6bf8d

Image Courtesy of Wikipedia

Check out this video by Minute Physics for a great overview of this.

What Does a Magnetic Field Look Like?

You may remember playing with magnets in elementary school, using a compass or iron filings to show the shape of the field. lines show the direction that the north pole of a magnet will be pushed or pulled. Just like electric charges, we can use the rule "likes repel, opposites attract". So, a north pole will repel other north poles and be attracted to south poles. Also, like electric fields, we can tell the strength of the field visually by looking at how close the lines are together.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-ubzK0ibyeyiR.gif?alt=media&token=06456cdb-1f77-440c-940a-3955888b3362

Image Courtesy of stickmanphysics

Here are some key points about how a magnetic dipole can be created:

  • A magnetic dipole is a that has two poles (north and south) and behaves like a tiny magnet.
  • A magnetic dipole can be created by separating the north and south poles of a magnet.
  • A magnetic dipole can also be created by placing a current-carrying wire in a . The will cause the charges in the wire to move, creating a north pole at one end of the wire and a south pole at the other end.
  • A magnetic dipole can be represented by a magnetic moment vector, which points from the south pole to the north pole and has a magnitude equal to the product of the pole strength and the distance between the poles.
  • The strength of a magnetic dipole decreases as the distance between the poles increases.
  • Magnetic dipoles can be used to model the magnetic fields of small magnets and current-carrying wires.

The Earth also produces a that protects us from a variety of . The charged particles from the spiral along the lines and collect around the poles resulting in . In order for this to occur, particles need to be charged to be affected by the Earth's .

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-a32WV943fXQj.jpeg?alt=media&token=ed8e90fe-94e1-45dd-814c-4ebf8b9fa3d9

Image Courtesy of wikipedia

strength is represented by B and has units of Tesla (T) where 1T = Ns / Cm. (Aren't you happy we can just write Tesla instead of Newton second per Coulomb meter? I am! 😄)

Magnetic Force from a Moving Charged Particle

So, why do charged particles curve in a ? They experience a force! The force from a can be calculated using this equation:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-ozwM6ecYC6uU.png?alt=media&token=cf98653e-6c96-4a61-ad97-e7a80a708dfa

Looking at this equation, we can see that in order to be affected by a magnetic force:

  1. The object must be charged (q ≠ 0)

  2. The particle must be moving (v ≠ 0)

  3. There must be a (B ≠ 0)

  4. The particle and the field must have a perpendicular component (cross product)

Ok, so we can calculate the magnitude of the force, but what about its direction? This can be easily found using the Right-Hand Rule (RHR). Point your thumb in the direction a positive charge is moving, your other fingers in the direction of the , and your palm will face the direction of the force.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-CYIehMJexrdi.jpg?alt=media&token=358ef731-c9db-4f03-88c9-c6a239444058

Image Courtesy of schoolbag.info

Magnetic Force from a Current in a Wire

So we've seen that a charge moving through a experiences a magnetic force. Let's apply the same concept to a wire and see what happens.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-ojwUGsM6qhSX.jpg?alt=media&token=dd7f88a4-8979-4657-ae0a-8909101476c0

Image Courtesy of cnx

Any wire with current passing through it becomes an electromagnet. The lines are circular around the wire radiating outwards. Again, we can use the right-hand rule to determine the direction of the . This application will be referred to as the Right-Hand Curl Rule (RHCR) since we now have 2 applications of this rule.

To do the RHCR, you position your hand with your thumb pointing in the direction of the current and curl your fingers around the wire. Your fingers point in the direction of the . In the example above, the $B$ field is coming out of the page to the left of the wire and going into the page on the right side of the wire.

The internal created by a very long current-carrying wire can be determined using the equation:

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-CPz0MA8gRaYE.png?alt=media&token=43b2b501-1010-4962-841e-899ef542453c

I is the current flowing through the wire, μo is the permeability of free space constant (found on the front page of your reference tables), and r is the distance away from the wire.

For a more detailed explanation of how this phenomenon works, check out part 2 of the Minute Physics video series on magnets.

Here are some key things to remember when drawing a :

  • A is a region around a magnet or electric current where the force of magnetism can be detected.
  • The direction of the at a particular point is the direction that a north pole of a magnet would point if it were placed at that point.
  • The strength of the at a particular point is related to the density of the field lines at that point. Field lines that are closer together indicate a stronger .
  • The lines around a magnet form closed loops, with the direction of the field given by the right-hand rule.
  • The lines around a current-carrying wire form concentric circles around the wire, with the direction of the field given by the right-hand rule.
  • When drawing a , it is important to pay attention to the direction of the field lines and the strength of the field at different points.
  • You can use a viewer (such as iron filings or a piece of paper with a magnet placed under it) to visualize the shape and direction of the .

Practice Questions

1.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-BA0dgvBrJmQZ.png?alt=media&token=26a71b44-7a41-42a7-a945-c73da74d4285

Image Courtesy of the AP Physics 2 Course & Exam Description

Answer

Choice B is correct. Use the Right Hand Rule twice. First to find the direction of the around the wire (should be coming out of the page above the wire, and into the page below the wire) then again to find the direction of the force the wire exerts on the charge (should be towards the the bottom of the page). The question asks for the force the charge exerts on the wire which is a Newton's 3rd Law pair with the force we just found. So the wire pushes the charge towards the bottom of the page and the charge pushes the wire towards the top of the page.

2. A negatively charged particle is moving with a speed of vo when it enters a region with B directed into the page. The dark curve shows the path the particle moved in the field.

https://firebasestorage.googleapis.com/v0/b/fiveable-92889.appspot.com/o/images%2F-ee1rP7Can0XP.png?alt=media&token=ddffa0a8-0241-4878-a4e5-dddff5f1fad9

What, if anything, is wrong with this diagram?

Answer

There are 2 major problems with this diagram

  • The particle should curve downwards not upwards in this field. The Right Hand Rule gives us a upwards force for a positive particle so the negative charge must experience a force downwards and therefore curve down towards the bottom of the page

  • The magnetic force is always perpendicular to the velocity of the particle, so the particle will always move in and move in an arc (1/4 of a circle) instead of the curve shown above.

Key Terms to Review (10)

Auroras

: Auroras are natural light displays that occur in the Earth's atmosphere, primarily near the polar regions. They are caused by interactions between charged particles from the sun (solar wind) and atoms or molecules in Earth's upper atmosphere.

Cosmic radiation

: Cosmic radiation refers to high-energy particles that originate from outside of Earth's atmosphere, such as protons and atomic nuclei. These particles can come from various sources in space, including the sun, distant stars, and even black holes.

Electron

: Electrons are subatomic particles that have a negative charge and orbit around the nucleus of an atom. They play a crucial role in determining the chemical properties and behavior of elements.

Magnetic domains

: Magnetic domains are small regions within ferromagnetic materials where groups of atoms align their magnetic fields in the same direction. These aligned domains contribute to the overall magnetization of the material.

Magnetic field

: A magnetic field is a region in space where a magnetic force can be detected. It is created by moving electric charges or by magnets.

Permeability of free space (μo)

: Permeability of free space refers to the measure of how easily a magnetic field can pass through a vacuum. It is a fundamental constant in physics that determines the strength and behavior of magnetic fields.

Right-Hand Rule (RHR)

: The Right-Hand Rule is a method used to determine the direction of magnetic fields, magnetic forces, and induced currents in wires.

Solar wind

: Solar wind refers to a continuous flow of charged particles (mainly electrons and protons) emitted by the sun into space. This stream of particles carries energy and magnetic fields throughout the solar system.

Tesla (T)

: Tesla is the unit used to measure the strength of a magnetic field. One tesla is equal to one newton per ampere-meter.

Uniform circular motion

: Uniform circular motion refers to the movement of an object in a circle at a constant speed, where its velocity is always changing due to its direction constantly changing.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.


© 2024 Fiveable Inc. All rights reserved.

AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.