# Transformation to a r. frame in which E and B are parallel

• egutierrezposse
In summary, the problem involves a static, uniform electric field and magnetic induction in a specific reference frame. The task is to determine the relative velocity of another reference frame where the electric and magnetic fields are parallel. A general Lorentz transformation is needed to solve the problem, specifically one that is not only in the z-axis. It can be shown that a boost in the z direction will yield the desired result.
egutierrezposse
This is problem 11.15 of Jackson, Classical Electrodynamics

In a certain reference frame a static, uniform, electric field Eo is parallel to the x axis, and a static, uniform, magnetic induction Bo = 2Eo lies in the xy plane, making an angle theta with the axis. Determine the relative velocity of a reference frame in which the electric and magnetic fields are parallel.

I need the resolution for a general Lorentz transformation (not-only in the z-axis)

Thanks

Hello, egutierrezposse. Welcome to PF!

According to forum rules, we need to see some attempt at a solution.

Try to convince yourself that a boost in the z direction will do the trick.

## 1. What is the significance of transforming to a reference frame where E and B are parallel?

Transforming to a reference frame where E and B are parallel can simplify certain calculations and make it easier to analyze electromagnetic phenomena. This transformation is particularly useful for studying electromagnetic waves.

## 2. How is the transformation to a parallel E and B reference frame performed?

The transformation involves changing the orientation of the coordinate axes so that E and B are parallel. This can be done by rotating the axes by a certain angle, which is determined by the relative directions and magnitudes of E and B.

## 3. Can any reference frame be transformed to have parallel E and B fields?

No, this transformation is only possible in certain cases. It is only applicable to reference frames where the relative directions and magnitudes of E and B are constant.

## 4. What are the advantages of using a parallel E and B reference frame?

Using a parallel E and B reference frame can simplify equations and make it easier to visualize and understand electromagnetic phenomena. It can also help identify patterns and relationships between E and B fields.

## 5. Are there any limitations to using a parallel E and B reference frame?

While this transformation can be useful, it is not always necessary or applicable. In some cases, it may not provide any additional insights or simplify calculations. Additionally, it may not be possible to transform to a parallel E and B reference frame in certain scenarios.

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