Mag. component of positive charges

[buddingscientist]

Hello scientists,

I'm unable to make any advances with this small problem.. two equal and positive charges (q) travel (in the same direction) at a speed (v), and are parallel to each other, at separation (r).
Derive an expression for the force between them, in the form of:
F = Felec(1 - [correction term]).
If anyone could shed some light on this or provide some insight it would be great thanks

 

[Tide]

There are three approaches you might try:

(a) Calculate both the magnetic field due to one of the charges at the location of the other charge then calculate the Lorentz force (electrostatic plus v cross B).

(b) Calculate the static electric field in a frame of reference moving along with the charges and then use the Lorentz transformation to find the electrostatic and magnetic fields in the stationary frame of reference.

(c) Same as (b) except you calculate the force in the moving frame and the use the Lorentz transform to find the force in the stationary frame.

I suspect you're interested in (a).

 

[buddingscientist]

Hmm thanks for the notes,
I get hints that I should use the Biot-savart law B = (mo/4p)(I.dL/r2) (m = mu, p = pi), and replace I.dL with data given in the question

 

[Tide]

Sounds like a great start!

 

[buddingscientist]

I'm still having some trouble relating the two :(

 

[Tide]

Think of the current as charge divided by a time interval and L as the speed times the time interval. The time interval will cancel out and you should get your magnetic field.

 

[buddingscientist]

Well..
B = (mo/4p)(qv/r^2)
I'm unfamiliar with how to connect it with 'F = Felec(1 - [correction term])'

Thanks a lot for the ideas and help by the way

 

[Tide]

If you learned about Biot-Savart then you should be able to determine the direction of the magnetic field. The magnetic force will be q v X b (vector cross product) which you will find is along a vector connecting the two charged particles (be careful with the signs). Finally, just add the electrostatic force.

 

[aekanshchumber]

take all forces in account, calculate them using integration (calculus).
I think answer is come with it.