Question

how much is the flux density at the centre of long solenoid​

Answer 1

Answer:

For a solenoid of length L = m with N = turns, the turn density is n=N/L= turns/m. The Earth's magnetic field is about half a gauss. The relative permeability of magnetic iron is around 200.

Answer 2

Answer:Current flowing through a conductor produces a magnetic field. If the conductor is a long straight wire, then the field is distributed over a large region of space.  

If the wire is used to make a coil, the magnetic field is concentrated into a smaller space and is therefore stronger.  

   

We could make some "educated guesses" at the factors affecting the magnitude of the flux density inside a solenoid:  

First, it must depend on the current flowing, I. Let's guess that it is directly proportional to the current (reasonable, as this is the case for a long straight conductor).  

It also seems likely that it will depend on the number of turns on the coil.  

However, consider the the first two coils shown below.

The coil on the right has twice as many turns as that on the left but is also twice as long.

Now, how about these two coils?

Again, the one on the right has twice as many turns as that on the left but those turns are concentrated into the same space so one might expect also a greater concentration of the magnetic field.  

So, we will suggest that the flux density depends not just on the number of turns but on the number of turns per unit length.  

Again, let's suggest a direct proportionality.  

These two factors are relatively easy to test by experiment and... wait for it... yes, our guesses are found to be correct!  

So we can write

Explanation: