Name: Magnetic Flux
Uploaded: 2019-07-19
Duration: 6 min 44 s
Description: Magnetic flux is the total number of magnetic lines of force that are passing through a given surface. To learn more about this intriguing concept, watch the...

Question

Obtain the expression for the mutual inductance of two long co-axial solenoids

S_{1}

and

S_{2}

wound one over the other, each of length

L

and radii

r_{1}

and

r_{2}

and

n_{1}

and

n_{2}

number of turns per unit length, when a current

I

is set up in the outer solenoid

S_{2}

.

Accepted Answer

Let $N_{1}$ and $N_{2}$ be the total number of turns of coils $S_{1}$ and $S_{2}$ , respectively.

When a current is $I$ is setup in the outer solenoid $S_{2}$ , it in turn sets up a magnetic flux through $S_{1}$ . Let us denote it by $ϕ_{1}$ .The corresponding flux linkage with solenoid $S_{1}$ will be

$N_{1} ϕ_{1} = M_{12} I$

Where $M_{12}$ is the mutual inductance of solenoid $S_{1}$ with respect to solenoid $S_{2}$ .

It is also referred to as the coefficient of mutual induction.

The magnetic field due to current $I$ in the solenoid $S_{2}$ is $μ_{0} n_{2} I$

The resulting flux linkage with solenoid $S_{1}$ is

$N_{1} ϕ_{1} = (n_{1} L) (π r_{1}^{2}) (μ_{0} n_{2} I)$

Where $n_{1} L$ is the total number of turns in solenoid $S_{1}$

$∴ M_{12} = μ_{0} n_{1} n_{2} π r_{1}^{2} L$

Note that we neglected the edge effects and considered the magnetic field $μ_{0} n_{2} I$ to be uniform throughout the length and width of the solenoid $S_{2}$ . This is a good approximation keeping in mind that the solenoid is long, implying $L ≫ r_{2}$ .

Obtain the expression for the mutual inductance of two long co-axial solenoids $S_{1}$ and $S_{2}$ wound one over the other, each of length $L$ and radii $r_{1}$ and $r_{2}$ and $n_{1}$ and $n_{2}$ number of turns per unit length, when a current $I$ is set up in the outer solenoid $S_{2}$ .

Important Questions on Electromagnetic Induction

Learn and Prepare for any exam you want !

Obtain the expression for the mutual inductance of two long co-axial solenoids S1 and S2 wound one over the other, each of length L and radii r1 and r2 and n1 and n2 number of turns per unit length, when a current I is set up in the outer solenoid S2.

Important Questions on Electromagnetic Induction

Learn and Prepare for any exam you want !

Obtain the expression for the mutual inductance of two long co-axial solenoids $S_{1}$ and $S_{2}$ wound one over the other, each of length $L$ and radii $r_{1}$ and $r_{2}$ and $n_{1}$ and $n_{2}$ number of turns per unit length, when a current $I$ is set up in the outer solenoid $S_{2}$ .