Can Parallel Charged Particles Maintain Their Speed in Space?

[sandy_cool]

Homework Statement

when two like charged particles are traveling in space on parallel tracks, exert electric and magnetic forces on each other, then what is their speed when they continue to move in the parallel track?

Homework Equations

since both are lick charges there should be a repulsive force, still can they travel parallel?

The Attempt at a Solution

lorentz force is present

 

[Simon Bridge]

Welcome to PF;
That's a good start.
By "tracks", does the question mean like railway tracks or just that the paths they are following are parallel at the instant being considered?

After that - just consider Newton's Laws.

 

[Astrum]

Homework Statement

when two like charged particles are traveling in space on parallel tracks, exert electric and magnetic forces on each other, then what is their speed when they continue to move in the parallel track?

Homework Equations

since both are lick charges there should be a repulsive force, still can they travel parallel?

The Attempt at a Solution

lorentz force is present

No attempt at the solution means that we can't really help you. Just a tip to add to what Simon Bridge has said, it can also help to draw a quick diagram to visualize the forces involved.

I may be missing something but... how can they be exerting force from their magnetic fields if they're both moving at the same $\mathbf v$ and are parallel? Something seems to be amiss in this problem. Did you make this one up?

To address your question "still can they travel parallel?", the author included the "tracks" to make sure that they could travel parallel. Typically, a problem like this is used to motivate the Maxwell Stress Tensor, the only difference is that the two charges are approaching the origin down the z and x-axis respectively.

As far as I can tell, the only force between them would be the electric fields.

 

[Simon Bridge]

I may be missing something but... how can they be exerting force from their magnetic fields if they're both moving at the same v and are parallel?

... works OK for two parallel wires when the currents are in the same direction though doesn't it?

It would help to know what level this question is posed at.

 

[Astrum]

... works OK for two parallel wires when the currents are in the same direction though doesn't it?

It would help to know what level this question is posed at.

I thought that because their relative velocity was zero, there would be no magnetic field.

This is why I like to preface my posts with "I may be missing something"

 

[WannabeNewton]

I thought that because their relative velocity was zero, there would be no magnetic field.

No this isn't how it works. We pick a background global inertial frame and we observe two parallel currents $I_1,I_2$ in this frame. Assuming steady state currents, both $I_1$ and $I_2$ generate respective magnetic fields $B_1,B_2$ in this frame as per Ampere's law for magnetostatics. Hence $I_2$ interacts with $B_1$ and $I_1$ interacts with $B_2$, as per the Lorentz force law, again as measured in said frame. What you're talking about is the situation in the rest frame of either one of the currents, which is a totally different story.

 

[sandy_cool]

By "tracks", does the question mean like railway tracks or just that the paths they are following are parallel at the instant being considered?

I mean parallel path in space.

 

[Simon Bridge]

OK - so you have two particles whose velocity vectors are parallel at t=0 ... the electric force will be pushing them apart - off parallel ... to keep moving parallel, they must be experiencing another force that pushes them together. (sketch the free body diagram for each particle...)

We've used the electric force - the only one left is magnetic.
What is the magnetic field of a charged particle moving at speed v?
How do you work out the magnetic force on a charged particle?