E & B Fields from Moving Charges: The Magnetic Monopole Mystery

[cragar]

Lets say I have a negative line charge on a long thin rod, if I am at rest with respect to that rod I will see an E field. But If I am moving with respect to that rod I will see a B field. So why are people looking for magnetic monopoles, If B fields are E fields in disguise, wouldn't the electrons need to show magnetic monopoles if they existed?

 

[tiny-tim]

hi cragar!

Lets say I have a negative line charge on a long thin rod, if I am at rest with respect to that rod I will see an E field. But If I am moving with respect to that rod I will see a B field.

yes, but it's only a tiny-weeny B field …

it's still mostly an E field ​

E²/c² - B² is invariant (the same in all frames), so since it's positive for the stationary rod, it's always positive

(if the speed is tanhu, then |E| = cE₀coshu and |B| = E₀sinhu)

similary, a stationary magnetic monople (if it exists) will have E = 0, and so E²/c² - B² will be negative, in that and any other frame …

there's no frame transformation that will turn pure E into pure B ​

 

[cragar]

I though it was E(dot)B that was invariant . Or is your way also equivalent. We can have frames where there is pure B then some E and B, but that probably doesn't help my case.

 

[tiny-tim]

I though it was E(dot)B that was invariant .

they're both invariant

see eg http://en.wikipedia.org/wiki/Electromagnetic_tensor#Properties"

(ooh, i forgot the 1/c factor in my previous answer …

i've gone back and corrected it )​