1. Flux density produced by a long coil (solenoid)
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
© D Hoult 2008

2. The flux density, Bc at the centre of a long coil, having N turns and of length L depends on

3. The flux density, Bc at the centre of a long coil, having N turns and of length L depends on
the current flowing through the solenoid, I

4. The flux density, Bc at the centre of a long coil, having N turns and of length L depends on
the current flowing through the solenoid, I
the number of turns per unit length

5. The flux density, Bc at the centre of a long coil, having N turns and of length L depends on
the current flowing through the solenoid, I
the number of turns per unit length
the permeability of the medium inside the solenoid

6. Experiments show that the flux density, Bc on the axis, at the centre of a solenoid is
directly proportional to I
directly proportional to N/L

7. I N
Bc a L

8. I N
Bc a L
The constant of proportionality is µ (the permeability of the medium), therefore we have

9. I N
Bc a L
The constant of proportionality is µ (the permeability of the medium), therefore we have
µ I N
Bc = L

10. The flux density on the axis at the end of the solenoid is equal to

11. The flux density on the axis at the end of the solenoid is equal to Bc / 2

12. The flux density on the axis at the end of the solenoid is equal to Bc / 2

13. The flux density on the axis at the end of the solenoid is equal to Bc / 2