Relation between Electric field and Magnetic field?

[Gaurav]

An observer in an inertial frame finds that at a point P the Electric field vanishes but the Magnetic field does not. This implies that in any other inertial frame the electric field E and the magnetic field B satisfy:
[these values in vectors]
1. |E|² = |B|²
2. E . B = 0
3. E x B = 0
4. E = 0

I know the answer is E.B = 0 but why is that?

 

[Orodruin]

What quantities (involving EM fields) do you know that are invariand under Lorentz transformations?

 

[Khashishi]

What is the relativistic definition of a scalar?

 

[Gaurav]

I don't know these values. This is a question of my exam. There is nothing given more.

 

[Orodruin]

If you do not know the expressions for the invariants of the electromagnetic field, then you have no chance (or rather 25% chance) to answer this question correctly. This suggests that your examiner expects you to know. Do you have some course litterature where you can look them up?

 

[Gaurav]

I have only its paper, I attached it, It is question no. 2 in it.

 

[Gaurav]

Its all I have

 

[Orodruin]

So I am assuming this is a general physics test of some sort. Your problem will not be solvable until you know some special relativity and how it describes the electromagnetic field. In order to fully understand the solution, you will also need to know what is meant by a Lorentz scalar and use some of the properties of the electromagnetic field tensor (see, e.g., http://en.wikipedia.org/wiki/Electromagnetic_tensor#Properties).

If you find the correct argumentation to use, this problem is solved in one line. In accordance with forum guidelines I will refrain from posting it here.

 

[Gaurav]

Thanks a lot. I will check it.

 

[Orodruin]

Just another small pointer: When they talk about a Lorentz invariant in the Wikipedia link above, this means that they are talking about a quantity which has the same value in all inertial frames. Given this information along with the Wikipedia information, you should be able to deduct the correct answer. Please tell me when you have figured it out and ask if you have further questions.

 

[Amit pokhriyal]

I'm still unable to get this relation. E.B =0
I guess for inertial frame, it should be easier

 

[SuvajitSardar]

An observer in an inertial frame finds that at a point P the Electric field vanishes but the Magnetic field does not. This implies that in any other inertial frame the electric field E and the magnetic field B satisfy:
[these values in vectors]
1. |E|² = |B|²
2. E . B = 0
3. E x B = 0
4. E = 0

I know the answer is E.B = 0 but why is that?

 

[berkeman]

@SuvajitSardar -- Welcome to PhysicsForums.

Please note that we generally don't allow the posting of full solutions to homework questions at PF (except for the OP). But in this case this thread is quite old, so it's okay that you posted your solution. I did not check it however.