Solving Magnetic Fields Produced by Multiple Charges in Free Space

AI Thread Summary
There is no single equation for calculating the magnetic field produced by multiple charges in free space because the problem is inherently complex. Instead, the magnetic fields from individual point charges can be summed, taking into account a retardation factor due to the finite speed of light. This means that changes in the magnetic field are delayed, affecting the overall calculation. In small regions, this time delay can often be considered negligible. Understanding these principles is crucial for accurately modeling magnetic fields in various scenarios.
martin f
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Why is there no equation for solving for the magnetic field produced by multiple charges in free space? To solve for this do you sum up all the magnetic fields produced by each of the point charges or what?
 
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martin f said:
Why is there no equation for solving for the magnetic field produced by multiple charges in free space? To solve for this do you sum up all the magnetic fields produced by each of the point charges or what?
That is correct. Maxwell's equations are linear, which means that the field produced by two point charges is just the sum of the fields from each individual charge.
 
martin f said:
Why is there no equation for solving for the magnetic field produced by multiple charges in free space? To solve for this do you sum up all the magnetic fields produced by each of the point charges or what?
Yes, if you add the magnetic fields up with a retardation factor. Changes in the magnetic field propagate at the speed of light. Therefore, changes in the electric current are retarded in the sense of having a delay.
For small regions, the time delay is negligible.
 
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