magnetic field

Examples of magnetic field in the following topics:

• Magnetic Field Lines

  • Magnetic field lines are useful for visually representing the strength and direction of the magnetic field.
  • Since magnetic forces act at a distance, we define a magnetic field to represent magnetic forces.
  • A pictorial representation of magnetic field lines is very useful in visualizing the strength and direction of the magnetic field .
  • The magnetic field is traditionally called the B-field.
  • Relate the strength of the magnetic field with the density of the magnetic field lines

• Paramagnetism and Diamagnetism

  • Paramagnetism is the attraction of material while in a magnetic field, and diamagnetism is the repulsion of magnetic fields.
  • The magnetic moment induced by the applied field is linear in the field strength; it is also rather weak.
  • When a magnetic field is applied, the dipoles will tend to align with the applied field, resulting in a net magnetic moment in the direction of the applied field.
  • These materials are slightly attracted by a magnetic field and the material does not retain the magnetic properties when the external field is removed, as illustrated in .
  • Diamagnetism is the property of an object or material that causes it to create a magnetic field in opposition to an externally applied magnetic field.

• Energy Stored in a Magnetic Field

  • When a conductor carries a current, a magnetic field surrounding the conductor is produced.
  • From Eq. 1, the energy stored in the magnetic field created by the solenoid is:
  • Therefore, the energy density $u_B = energy / volume$ of a magnetic field B is written as $u_B = \frac{B^2}{2\mu}$.
  • Magnetic field created by a solenoid (cross-sectional view) described using field lines.
  • Energy is "stored" in the magnetic field.

• Helical Motion

  • Helical motion results when the velocity vector is not perpendicular to the magnetic field vector.
  • What if the velocity is not perpendicular to the magnetic field?
  • The component of the velocity parallel to the field is unaffected, since the magnetic force is zero for motion parallel to the field.
  • shows how electrons not moving perpendicular to magnetic field lines follow the field lines.
  • Describe conditions that lead to the helical motion of a charged particle in the magnetic field

• Ferromagnets and Electromagnets

  • In the second class of magnets—known as electromagnets—the magnetic field is generated through the use of electric current.
  • If the current disappears, the magnetic field is turned off.
  • An electric current flowing in a wire creates a magnetic field around the wire.
  • The magnetic field from all the turns of wire passes through the center of the coil creating a strong magnetic field there.
  • Current (I) through a wire produces a magnetic field (B).

• Electric vs. Magnetic Forces

  • In contrast, recall that the magnetic force on a charged particle is orthogonal to the magnetic field such that:
  • where B is the magnetic field vector, v is the velocity of the particle and θ is the angle between the magnetic field and the particle velocity.
  • If the particle velocity happens to be aligned parallel to the magnetic field, or is zero, the magnetic force will be zero.
  • The curl of a magnetic field generated by a conventional magnet is therefore always non zero.
  • Magnetic fields exert forces on moving charges.

• Magnetic Force on a Current-Carrying Conductor

  • When an electrical wire is exposed to a magnet, the current in that wire will experience a force—the result of a magnet field.
  • When an electrical wire is exposed to a magnet, the current in that wire will be affected by a magnetic field.
  • The force (F) a magnetic field (B) exerts on an individual charge (q) traveling at drift velocity vd is:
  • In this instance, θ represents the angle between the magnetic field and the wire (magnetic force is typically calculated as a cross product).
  • Express equation used to calculate the magnetic force for an electrical wire exposed to a magnetic field

• Magnitude of the Magnetic Force

  • The magnetic force on a charged particle q moving in a magnetic field B with a velocity v (at angle θ to B) is $F=qvBsin(\theta )$.
  • Magnetic fields exert forces on moving charges, and so they exert forces on other magnets, all of which have moving charges.
  • The magnitude of the magnetic force $F$ on a charge $q$ moving at a speed $v$ in a magnetic field of strength $B$ is given by:
  • The Earth's magnetic field on its surface is only about 5×10−5 T, or 0.5 G.
  • Magnetic fields exert forces on moving charges.

• Permanent Magnets

  • Permanent magnets are objects made from ferromagnetic material that produce a persistent magnetic field.
  • Recall that a magnet is a material or object that generates a magnetic field.
  • A permanent magnet is an object made from a material that is magnetized and creates its own persistent magnetic field .
  • In response to an external magnetic field like the one applied in the above figure, these regions grow and become aligned.
  • The magnet is made in the shape of a horseshoe to bring the two magnetic poles close to each other, to create a strong magnetic field there that can pick up heavy pieces of iron.

• Ferromagnetism

  • In response to an external magnetic field, the domains may grow to millimeter size, aligning themselves.
  • Permanent magnets (materials that can be magnetized by an external magnetic field and remain magnetized after the external field is removed) are ferromagnetic, as are other materials that are noticeably attracted to them.
  • The quantum mechanical nature of this spin limits the electron to only two states: with the magnetic field pointing either "up" or "down" (for any choice of up and down).
  • When these tiny magnetic dipoles are aligned in the same direction, their individual magnetic fields combine to create a measurable macroscopic field.
  • (b) When magnetized by an external field, the domains show greater alignment, and some grow at the expense of others.