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Solved Problems-7

Problems-7
Prove that the magnetic scalar potential at (0, 0, z) due to a circular loop of radius ‘a’ is, Description: Description: 106633.png.
 
Circular current-carrying loop
 
Solution
We have the magnetic field at (0, 0, z) due to the circular loop of radius a is given as,
Description: Description: 159477.png
 
Comparing both sides,
Description: Description: 106617.png
 
Integrating,
Description: Description: 106606.png
 
Let, Description: Description: 106598.png
Description: Description: 106589.png
z z
θ Description: Description: 106574.png  A
Here, Description: Description: 106559.png 
Description: Description: 106552.png
 
Putting the value Description: Description: 106545.png we get,
∴  Description: Description: 106538.png
 




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