Tajimura said:In a moving reference frame the line charge and the point charge are not moving relative to each other, so the charge will not "feel" any magnetic field.
Yup, you are right. It just rained down on me after I send the answer and left the forum, that relative speed of charges bears no importance here. Magnetic force is just a relativistic effect of changing a reference frame, and though moving observer is observing additional magnetic force, electric force observed by him is less than the electric force observed by stationary observer, so full force is just the same in both cases.Orodruin said:This is irrelevant, the charge is moving and there is a magnetic field, so the charge will be subjected to a magnetic force. What needs to be realized is that magnetic and electric fields, and therefore forces, transform into each other under Lorentz transformations.
Just insert linear change field into Lorentz transformations with burst v and see how the field get transformed into linear combination of electric and magnetic fields.brianeyes88677 said:Can anyone do it mathematically?
The magnetic force in a moving coordinate system is the force exerted on a charged particle due to its motion in a magnetic field. It is perpendicular to both the direction of the particle's motion and the direction of the magnetic field.
The magnetic force in a moving coordinate system is calculated using the formula F = qv x B, where q is the charge of the particle, v is its velocity, and B is the strength of the magnetic field. The x symbol represents the vector cross product, which takes into account the perpendicular nature of the force.
The magnitude of the magnetic force in a moving coordinate system remains the same, but its direction may change as the particle moves in different directions and the magnetic field changes. This is because the force is always perpendicular to the particle's motion and the magnetic field.
The magnetic force in a moving coordinate system can cause a charged particle to change its direction of motion, but it does not affect its speed. The particle will move in a circular or helical path, depending on the strength and direction of the magnetic field.
The magnetic force in a moving coordinate system is used in a variety of applications, such as particle accelerators and mass spectrometers, to manipulate and control the motion of charged particles. It is also important in understanding the behavior of charged particles in Earth's magnetic field, which is crucial for space exploration and satellite navigation systems.