Magnetic field of uniform strength at all points inside a solenoid?

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fiziksfun
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simple question:

is the magnetic field of uniform strength at all points inside a solenoid?
 
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best answer:

How would you try to figure this out?

simple answer:

Yes, if the solenoid is infinite in length and the current density is uniform. Use the "best answer" to try to figure out why "simple answer" is true. What physical law would you use?