# Finding Magnetic Field using Lorentz Force

• derrickb
In summary, to determine the magnetic field B at a fixed point, two measurements of magnetic force F1 and F2 are sufficient, provided that the velocities v1 and v2 are orthogonal. This means that only the x and y components of the velocities are needed, as there is no force in the z-direction. The contributions of each component of F can be determined by the cross-product, with Fz = qv_x B_y - qv_y B_x. This relationship between F and B is also seen in the fact that qv x B = -B x qv.
derrickb

## Homework Statement

Show that two measurements F1 and F2 of magnetic force at a fixed point are sufficient enough to determine B at that point as (see picture) provided v1 and v2 are orthogonal.

2. Homework Equations

F = qv x B
Bz = cFx/(qvy)
By = cFz/(qvx)
Bx = cFy/(qvz)

## The Attempt at a Solution

I have 3 pages of various attempts that I can upload if necessary. I can't seem to figure out what the orthogonality has anything to do with and to be honest, the professor wrote this down on the board and he could have forgotten an exponent or something like that. If someone could even just give me a hint as to what the orthogonal velocities has anything to do with, I may be able to figure it out from there.

#### Attachments

• image2.JPG
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he means that you only need v_x and v_y , if you know all components of their Forces

I'm a little confused by what you're saying. Why don't you need the z-components of the velocities?

Nevermind I just remembered there is no force caused by the velocity in the direction of the field. So you mean you only need v_x and v_y if B is in the z-direction?

If F_1,z is applied to qv_x , what does that tell you? (yes, B_y)
If F_2,z is applied to qv_y , what does that tell you? (your original post doesn't have this)

That would tell you B_x?

actually its negative.
Each component of F has 2 contributions from each cross-product. example: F_z = qv_x B_y - qv_y B_x
(OMG! qv x B = - B x qv ! is this cool?)

## 1. How is the Lorentz force used to find magnetic field?

The Lorentz force, given by the equation F = qvB, is used to find the magnetic field by measuring the force exerted on a charged particle moving with a known velocity in a magnetic field.

## 2. What is the relationship between Lorentz force and magnetic field?

The Lorentz force is directly proportional to both the magnetic field strength and the velocity of the charged particle, and is perpendicular to both the magnetic field and the particle's velocity.

## 3. What is the difference between finding magnetic field using a current-carrying wire and using a charged particle?

When finding magnetic field using a current-carrying wire, the magnetic field is created by the current flowing through the wire. However, when using a charged particle, the magnetic field is external and the particle is simply experiencing the force due to its motion in the field.

## 4. How does the direction of the Lorentz force help determine the direction of the magnetic field?

The direction of the Lorentz force is always perpendicular to both the magnetic field and the velocity of the particle. Therefore, by measuring the direction of the force, the direction of the magnetic field can be determined using the right-hand rule.

## 5. What are some real-life applications of finding magnetic field using Lorentz force?

Finding magnetic field using Lorentz force is used in various technologies, such as particle accelerators, mass spectrometers, and magnetic resonance imaging (MRI) machines. It is also used in navigation systems, such as the compass, which relies on the Earth's magnetic field to determine direction.

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