Magnetic Flux

Magnetic Flux

In the beginning of the nineteeth century, Oersted discovered that a magnetic field exists around a current carrying conductor. We can say that magnetism can be produced by the means of an electric current. In 1831, Faraday discovered that magnetic field can create an electric current. The process of producing an electric current from the magnetic field when the conductor forms a complete loop or circuit is called electromagnetic induction.

To demonstrate the phenomenon of electromagnetic induction consider a coil of several times connected to a galvanometer. If a permanent magnet is moved towards the coil, it will be observed that the galvanometer shows deflection in one direction. In

Magnetic Flux

Magnetic flux \((\phi )\) through any surface is defined as the number of magnetic lines of forcecrossing through that surface .

Consider a small surface are A.a normal is drawn to the surface. If \(\theta \) be the angle between normal and uniform magnetic field as shown in figure, then the magnetic flux \((\phi )\) through the surface is defined as

$$\begin{align*} \phi &= \vec B . \vec A= BA\cos \: \theta \\ \text {or,} \: \phi &=(B\: \cos \: \theta ) A \dots (i) \\ \end{align*}$$

Now \(B\cos \: \theta \) is the component of the magnetic field normal to the plane of the surface and can be represented by B_n­. so equation (i) becomes,

$$ \phi = B_n A \dots (ii) $$

Thus, magnetic flux over a given surface is defined as the product of the area of the surface and normal component of magnetic field.

Special cases

1. When \(\theta = 0^o \), i.e. uniform magnetic field is acting perpendicular to the plane of the suface, then,\(\phi = BA\cos \: 0^o\) = BA which is maximum.
2. When \(\theta = 90^o \) i.e.. uniform magnetic field is along the surface is then \(BA\cos \: 90^o = 0\) which is minimum.

Unit of Magnetic Flux

In SI, the magnetic flux measured in Weber (Wb).

$$\begin{align*} \text {Since,} \: \phi = B_nA \\1 \: \text {Weber} = 1 \: \text {tesla} \times 1\: m^2 = 1 T m^2 \\ \text {In CGS-system, unit of magnetic flux is Maxwell.} \\ 1 \: \text {Maxwell} = 10^{-8} \: \text {Weber} \\ \end{align*}$$

Dimensional formula of Magnetic Flux

We know,

$$\begin{align*} \phi = BA \: \cos\: \theta \\ \text {Since,} \: B = \frac {F}{qv} \: \text {and } \: \cos \: \theta \: \text { is dimensionless. So} \\ \phi &= \frac {FA}{QV} = \frac {FA}{ItV} \:\:\: [ \because I = \frac qt \rightarrow q = it ] \\\frac {[F][A]}{[I]\: [t]\:[v]} &= \frac {[MLT^{-2}][L^2]}{[A][T][LT^{-1}]} \\ \therefore \: [\phi ] &= [ML^2T^{-2} A^{-1}] \\\end{align*}$$

Magnetic flux \((\phi )\) is a scalar quantity.