Magnetic force between two parallel moving charges

Click For Summary
When two charges move parallel to each other at equal speeds, they do not experience a magnetic force from each other in their own reference frame, as they are at rest relative to one another. However, in a different reference frame, such as a laboratory frame, they are moving and thus can experience both electric and magnetic forces. The magnetic force arises due to their motion relative to the observer, while the electric force remains repulsive. The interaction is complex, as the forces can be viewed differently depending on the observer's frame of reference, with relativistic effects modifying the perceived strength of these forces. Ultimately, the relationship between electric and magnetic forces is unified through the principles of relativity.
  • #31
Exactly so. When psi = pi/2, i.e. in the transverse direction, (1 - beta^2 sin^2 psi)^3/2 becomes (1 - beta^2 )^3/2 = gamma^-3, so the transverse E in the lab frame is simply gamma times that in the rest frame of an electron. We can reach this result very simply by applying length contraction to a coin-shaped gaussian box with an electron at its centre.
 

Similar threads

Undergrad Magnetic field as result of length contraction
  • · Replies 20 ·
Replies
20
Views
5K
Undergrad Question on Hall Effect and magnetic force
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad The vector math of relative motion of wire-loop & bar magnet
  • · Replies 1 ·
Replies
1
Views
2K
High School Applying the Gauss (1835) formula for force between 2 parallel DC currents
  • · Replies 6 ·
Replies
6
Views
575
Why Doesn't Electric Force Cause Wires to Move?
  • · Replies 15 ·
Replies
15
Views
2K
Undergrad Charge movement relative to magnetic field frame dependence/invariance
  • · Replies 5 ·
Replies
5
Views
1K
Current and stationary charges
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Does a Railgun's Current Violate Conservation of Momentum?
  • · Replies 61 ·
3
Replies
61
Views
5K
Undergrad Railgun: Significant magnetic field where projectile is?
  • · Replies 8 ·
Replies
8
Views
2K
The work of magnetic force on the wire
  • · Replies 12 ·
Replies
12
Views
3K