Question

The inductance of a closely packed coil of 400 turnsis 8.0 mH. Calculate the magnetic flux through the coil when the current is 5.0 mA.

Short answer

Magnetic flux through the coil is $1.0\times {10}^{-7}\mathrm{Wb}$.

Step-by-step solution

Given

I) Number of turns of coil ,$N=400$

ii) Inductance of coil ,$L=8.0\times {10}^{-3}H$

iii) Current through the coil ,$i=5.0\times {10}^{-3}A$

Determining the concept

Magnetic flux though the coil is proportional to the current flowing though that coil and the proportionality constant is the inductance of that coil. Inductance of coil depends on the size and shape of coil, and also on the number of turns of the coil.

Formulae are as follow:

Magnetic flux ,${\varphi }_B=Li$

Magnetic flux through the coil having N turns,$\varphi =N{\varphi }_B$

Where,${\Phi }_B$is magnetic flux, iis current, L is inductance, N is number of turns.

Determining the magnetic flux through the coil

Magnetic flux through the coil is,

$$\begin{gathered} \varphi =Li \\ \varphi =(8.0\times {10}^{-3}H\times 5.0\times {10}^{-3}A)=40\times {10}^{6}HA \\ {\varphi }_B=\frac{\varphi }{N}=\frac{40\times {10}^{6}HA}{40} \\ {\varphi }_B=1.0\times {10}^{-7}Wb \end{gathered}$$

Hence, Magnetic flux through the coil is $1.0\times {10}^{-7}\mathrm{Wb}$.

Therefore, by using the concept of magnetic field and inductance, magnetic flux through the coil can be determined.