# Electromagnetism question, what formula

• fluidistic
In summary, the conversation discusses the use of a formula to find the effects of a uniform magnetic field on a moving object. It also mentions the importance of using a Lorentz transformation to calculate the electric and magnetic fields in different reference frames. The formula for the transformation is provided, along with explanations of the variables involved. The conversation concludes with the suggestion to learn this topic in preparation for a future course.
fluidistic
Gold Member
I'd like to know what formula to use in order to find the following :
Imagine a uniform magnetic field. I am moving with a constant velocity perpendicularly through it. Do I see only an electric field? A magnetic field? Both? Or both of them?
What if I move in the sense of the magnetic field with a constant velocity?

What if my velocity changes with time?
What if, instead of the magnetic field, it's an electric field?

I do not expect the answer to all these questions, rather I'd like a formula to check it out myself. But if you have to say a word or even give the answer, I'm all ears.

What velocity are you traveling with? If it's much lower than the speed of light:

Pythagorean said:
What velocity are you traveling with? If it's much lower than the speed of light:

Thanks a lot. I'm a bit confused, if B is uniform, if I move, $$\frac{\partial B}{\partial t}=0$$ or I'm wrong?

To look at EM in another velocity you need to use a lorentz transformation of the field. If you are familiar with vectors, J.D. Jackson p. 558 gives a useful form:

$$\vec{E}' = \gamma (\vec{E} + \vec{\beta} \times \vec{B}) - \frac{\gamma^2}{\gamma + 1} \vec{\beta} (\vec{\beta} \cdot \vec{E})$$

$$\vec{B}' = \gamma (\vec{B} - \vec{\beta} \times \vec{E}) - \frac{\gamma^2}{\gamma + 1} \vec{\beta} (\vec{\beta} \cdot \vec{B})$$

$$\vec{\beta} = \vec{v}/c$$
$$\gamma = \frac{1}{\sqrt{1 - \beta^2}}$$

So, you see if you have one frame where E = 0, and only B != 0. Then in every other frame E' != 0, and B' != 0, since B appears in both terms.

kcdodd said:
To look at EM in another velocity you need to use a lorentz transformation of the field. If you are familiar with vectors, J.D. Jackson p. 558 gives a useful form:

$$\vec{E}' = \gamma (\vec{E} + \vec{\beta} \times \vec{B}) - \frac{\gamma^2}{\gamma + 1} \vec{\beta} (\vec{\beta} \cdot \vec{E})$$

$$\vec{B}' = \gamma (\vec{B} - \vec{\beta} \times \vec{E}) - \frac{\gamma^2}{\gamma + 1} \vec{\beta} (\vec{\beta} \cdot \vec{B})$$

$$\vec{\beta} = \vec{v}/c$$
$$\gamma = \frac{1}{\sqrt{1 - \beta^2}}$$

So, you see if you have one frame where E = 0, and only B != 0. Then in every other frame E' != 0, and B' != 0, since B appears in both terms.

Ok thank you very much. I'm going to try to grasp this. I took vector calculus. I'm taking the 1 year EM course on next term (in March). I thought I would need it for the intro to EM course, but I'm not sure now. Anyway, I'll do an effort to learn this part.

## 1. What is the formula for calculating the strength of an electromagnet?

The formula for calculating the strength of an electromagnet is F = (N x I)^2 x μ0 x A / (2 x g^2), where F is the force in Newtons, N is the number of turns in the coil, I is the current in Amps, μ0 is the permeability of free space, A is the cross-sectional area of the coil, and g is the distance between the coil and the object being attracted.

## 2. How do you calculate the force between two charged particles?

The force between two charged particles is calculated using F = (k x q1 x q2) / r^2, where F is the force in Newtons, k is the Coulomb's constant (9 x 10^9 Nm^2/C^2), q1 and q2 are the charges of the two particles in Coulombs, and r is the distance between the two particles in meters.

## 3. What is the formula for determining the direction of the magnetic field around a current-carrying wire?

The formula for determining the direction of the magnetic field around a current-carrying wire is given by the right-hand rule. If the thumb of your right hand points in the direction of the current flow, then the direction of the curled fingers will indicate the direction of the magnetic field.

## 4. How is the strength of an electric field calculated?

The strength of an electric field is calculated using E = F / q, where E is the strength of the electric field in Newtons per Coulomb, F is the force acting on the charged particle in Newtons, and q is the magnitude of the charge on the particle in Coulombs.

## 5. What does Faraday's Law state?

Faraday's Law states that the induced electromotive force (EMF) in a closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit. It is represented by the formula EMF = -N(dΦ/dt), where N is the number of turns in the coil, Φ is the magnetic flux in Webers, and t is the time in seconds.

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