I have learnt that the formula for calculating the magnetic field at the centre of a current-carrying coil of N turns is:- B=μNI2r
(where r= radius of the loop, I= current in the coil) And, the magnetic field at the centre of a current-carrying solenoid of N turns is:- B=μNIL
(where L & I are the length and the current in the solenoid respectively and μ=μ0μr is the magnetic permeability).
As we can see, both these formulas are different. But I can't figure out why that is. (Since from what I have read about solenoids, they are just a number of coils wound closely together).
So my question is- why are there two different formulas for magnetic field at the the centre of a coil of N turns and of a solenoid? (Is a solenoid somehow different from a coil having many turns?)
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