Lorentz Force in conductive beam

In summary: It is known that in a current carrying wire, exposed to a magnetic field, the wire will experience a force equal to the product of the field, the current and the length of the wire (where the direction of the force is orthogonal to both the field and the direction along the length of the beam). F = B*I*LNow, in a rectangular beam of length L, width w, and height h (where w<<h<<L), again carrying a current and in the presence of a magnetic field, how is the Lorentz force expressed? is the force acting as a distributed load all along the beam? is this integrated force modeled as a point load at the center of the beam? Is it acting
  • #1
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It is known that in a current carrying wire, exposed to a magnetic field, the wire will experience a force equal to the product of the field, the current and the length of the wire (where the direction of the force is orthogonal to both the field and the direction along the length of the beam). F = B*I*L

Now, in a rectangular beam of length L, width w, and height h (where w<<h<<L), again carrying a current and in the presence of a magnetic field, how is the Lorentz force expressed? is the force acting as a distributed load all along the beam? is this integrated force modeled as a point load at the center of the beam? Is it acting as a body load? a surface load? Could someone help me understand this??

Thanks in advance,

diemilio
 
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  • #2
diemilio said:
It is known that in a current carrying wire, exposed to a magnetic field, the wire will experience a force equal to the product of the field, the current and the length of the wire (where the direction of the force is orthogonal to both the field and the direction along the length of the beam). F = B*I*L

Now, in a rectangular beam of length L, width w, and height h (where w<<h<<L), again carrying a current and in the presence of a magnetic field, how is the Lorentz force expressed? is the force acting as a distributed load all along the beam? is this integrated force modeled as a point load at the center of the beam? Is it acting as a body load? a surface load? Could someone help me understand this??

Thanks in advance,

diemilio

In such a case the force is distributed, and it would be important to know the current density (current per unit area) in the beam. For a low frequency, or direct current, you may be able to approximate the current density distribution as constant across the beam, but it really depends on the material properties and how the voltage is applied to the ends of the beam.

In general the force would be expressed as an integral over the volume of the beam. The Lorenz force is really force per unit length, and the surface integral is taken over the cross section in terms of current density J, rather than current I.
 
  • #3
Nice! Got it! Thank you so much for the quick reply!

diemilio
 

1. What is the Lorentz Force in a conductive beam?

The Lorentz Force is the force exerted on a charged particle in a conductive beam when it moves through a magnetic field. This force is perpendicular to both the direction of the particle's motion and the direction of the magnetic field.

2. How is the Lorentz Force calculated?

The Lorentz Force is calculated using the equation F = q(v x B), where F is the force, q is the charge of the particle, v is its velocity, and B is the magnetic field strength. This equation is a vector cross product, meaning the force is perpendicular to both v and B.

3. What factors affect the Lorentz Force in a conductive beam?

The strength of the magnetic field, the charge of the particle, and the velocity of the particle all affect the Lorentz Force. Additionally, the angle between the particle's velocity and the direction of the magnetic field can also impact the force.

4. What are some practical applications of the Lorentz Force in conductive beams?

The Lorentz Force is used in a variety of technological applications, such as particle accelerators, mass spectrometers, and cathode ray tubes. It is also essential in understanding the behavior of electric currents in conductive materials.

5. What is the relationship between the Lorentz Force and the Hall Effect?

The Hall Effect is a phenomenon where a voltage is generated across a conductor when a magnetic field is applied perpendicular to the direction of current flow. This effect is caused by the Lorentz Force acting on the moving charges in the conductor. Therefore, the Lorentz Force and the Hall Effect are closely related.

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