Solving Magnetic Field Force: Observer I vs Observer II

• physicsManiac
In summary: That's correct! In summary, both observers see the same physics when observing charges moving parallel to the y-axis, but an accelerating observer sees a different force than a non-accelerating observer.

physicsManiac

i have 2 questions regarding magnetic field...
1)if 2 identical charges move parallel to each other(along y axis) with relative velocity zero the the observer I moving along with the charges will observe force along one direction only(along x-axis electrostatic) whereas an observer II(standing at origin) watching the charges move away will observe a force on charges along both x and y direction(x and y-axis both i.e magnetic and electrostatic).So what is the correct observation?

2)what will happen if one frame is accelerating ie observer II.

welcome to pf!

hi physicsManiac! welcome to pf!
physicsManiac said:
1)if 2 identical charges move parallel to each other(along y axis) with relative velocity zero the the observer I moving along with the charges will observe force along one direction only(along x-axis electrostatic) whereas an observer II(standing at origin) watching the charges move away will observe a force on charges along both x and y direction(x and y-axis both i.e magnetic and electrostatic).So what is the correct observation?

if the speed is tanhα, then observer II measures the field as Ey = Ecoshα, Bz = Esinhα.

since the x component of velocity is tanhα, the total force (per unit charge) in the y direction is Ecoshα - Esinhαtanhα, = Esechα, which combined with time dilation gives us the same as the original E

(that still leaves a magnetic force in the x direction, which curves the path away from the "vertical" … but that's ok because for observer II the charges are not moving parallel to the y-axis, and the faster they move, the greater the angle to the y-axis )
2)what will happen if one frame is accelerating ie observer II.

uhh? why would anyone want to make calculations relative to an accelerating frame?

physicsManiac said:
So what is the correct observation?

I would say that both observations are equally correct. The same physics happens, just described in different ways.

Wasn't this essentially one of the thought experiments Einstein used to find the Lorentz transformation formulas by the way?

1. What is the difference between Observer I and Observer II in solving magnetic field force?

Observer I and Observer II refer to two different approaches in solving for magnetic field force. Observer I uses the Biot-Savart law, which is based on the contributions of individual current elements, while Observer II uses Ampere's law, which is based on the total current passing through a closed loop.

2. Which approach is more accurate in solving magnetic field force?

Both approaches have their own limitations and assumptions, so it ultimately depends on the specific situation. Observer I is more accurate for calculating the magnetic field at a specific point near a current-carrying wire, while Observer II is more accurate for calculating the magnetic field inside a current-carrying solenoid.

3. Can both approaches be used interchangeably?

No, they cannot be used interchangeably as they are based on different laws and have different applications. Using the wrong approach can lead to incorrect results.

4. What factors affect the strength of the magnetic field force?

The strength of the magnetic field force depends on the magnitude and direction of the current, the distance from the current, and the properties of the medium through which the current is passing.

5. How can the magnetic field force be calculated for a complex system?

For a complex system, the magnetic field force can be calculated by breaking it down into smaller, simpler components and using either Observer I or Observer II to solve for the magnetic field at each point. The resultant magnetic field at a given point is the vector sum of the individual magnetic fields from each component.