Magnetic Flux of a Solenoid

Introduction to magnetic flux of a solenoid
A solenoid consists of an insulating long wire closely wound in the form of a helix. Its length is very large as compared to its diameter. In a magnetic field the total number of magnetic lines of force crossing the solenoid measures the magnetic flux through any solenoid holds. To find the magnetic flux of a solenoid first we find the amount of magnetic field in a current carrying solenoid.

Please express your views of this topic Electric and Magnetic Fields by commenting on blog.

Magnetic field in a solenoid to find the magnetic flux of a solenoid


Consider a long solenoid of circular crossection. Let the number of turns per unit length is n and the current flowing in the solenoid id I. Now according to the Ampere’s circuital law, the amount of magnetic field linked across a solenoid is

B = `mu`0nI, where `mu`0 is the absolute permeability of free space.

This amount of magnetic filed is well inside the solenoid. The amount of magnetic field at the end of the solenoid is `mu`0nI/2. The magnetic field is a vector quantity, the SI unit of magnetic field is Tesla, and the CGS unit is Gauss. The relation between Tesla and gauss is

1Testla = 10000 Gauss


Magnetic flux of a solenoid


The number of magnetic lines of force crossing through the solenoid is called the magnetic flux linked with the solenoid. Let the magnetic field linked across the solenoid is B and the area of the crossection is A, then the amount of magnetic flux linked with the solenoid is

`phi`  = B A Cos `theta` , where `theta` is the angle between the magnetic field vector and the area vector.

As we know that the magnetic field across the solenoid is B = `mu`0nI, so the magnetic flux linked across the solenoid is

`phi` = `mu`0nIA Cos `theta`, here if the angle between the magnetic field vector and the area vector is 0°, then the maximum magnetic flux linked with the solenoid is

`phi`= `mu`0nIA

I have recently faced lot of problem while learning Equation for Force, But thank to online resources of science which helped me to learn myself easily on net.

Magnetic flux of a Solenoid : Conclusion.


The magnetic flux is the dot product of magnetic field and the area vector so the magnetic flux is the scalar quantity. According to the formula of magnetic flux of a solenoid, we can conclude that the magnetic flux depends on the number of turns per unit length, amount of electric current flowing through the solenoid and the area of crossection of the solenoid.