Magnetic Flux Formula

It's the component of the flux that passes through the coil that's shared by all. Magnetic flux is represented by the symbol B, where B could be a field and therefore the unit is Weber (Wb). The magnetic flux value could be a vector quantity that depends on the flux direction.

Magnetic flux refers to the total number of magnetic field lines penetrating any surface placed perpendicular to the magnetic field. It is calculated as the product of the average magnetic field strength and the perpendicular area it penetrates. 

Magnetic flux is denoted by ΦB where B represents magnetic field, and its unit is tesla-meter2 or weber (Wb).

Mathematically, the magnetic flux formula is as follows:

\[\Phi B=\vec{B}.\vec{A}\Phi B=B\rightarrow .A\rightarrow \]

Or,

\[\Phi B=BAcos\theta \]

Where, B is the magnetic field of force, A is the surface area or extent and θ is the angle between the normal to the surface and the magnetic field.

If a coil of n turns and area of cross section A is placed in a magnetic field of strength B, then the total flux associated with the coil is:

\[\Phi B=nBAcos\theta \]

Solved Examples

1. A magnetic field of 2.5 T passes perpendicular to a disc of radius 2 cm. Find the magnetic flux associated with the disc.

Solution: B = 2.5 T, r = 2 cm = 2 × 10–2 m, θ = 0,

\[\Phi B=?\Phi B=BAcos\theta =2.5\times \pi (2\times 10^{-2})2\times cos0=3.14\times 10^{-3}Wb\]

2. A coil of area of cross section 10–2 m2 and 100 turns is placed in a magnetic field of strength 1 T, with its axis making an angle 60° with the field. Find the total flux associated with the field.

Solution: B = 1 T, A = 10–2 m2,

\[\theta =60^{\circ},n=100,\Phi B=?\Phi B=nBAcos\theta =100\times 1\times 10^(-2)\times cos60^{\circ}=0.5Wb\]

3. When the coil is rotated between the pole pieces of a magnet as shown, during one complete rotation of the coil, how often will the magnetic flux linked with the coil be maximum and minimum?

Options:

(a) maximum and minimum once each

(b) maximum and minimum twice each

(c) maximum once, minimum twice

(d) maximum twice, minimum once

Answer: (b)

Magnetic Properties of Electricity flowing through a Wire

As a child, you must all have played with a magnet. It is a material that attracts iron or ferrous objects. Chromium and Nickel are the other two objects that are attracted to magnets. Later when the characteristics of a magnet were discovered it was found that in the magnet there exist two poles at both ends. One pole is known as the north pole and the other is the south pole. In later days it also has been discovered that the electric when passing through a metal wire also possesses characteristics of magnetism in it. And if the wire is turned in a form of spring or selenium and electric current is passed through it then the spring behaves like an actual magnet. The north pole and south pole of this type of magnet can be easily identified by the use of a compass.

The magnetic force of any normal magnet or an electromagnet can be represented by magnetic lines. These magnetic lines originate from the north pole of the magnets and end at the south pole of the magnet completing a closed circuit through the body of the magnet. When a ferrous object is brought near a magnetic object then it also behaves like a  magnet. The quality of magnetic property of such a magnet depends on the number of magnetic lines of force passing through this object that originate from the actual magnet. The measurement of the quantity of the magnetic force experienced by any object is measured by the magnetic lines of force entering and exiting it. The term used to describe this measurement is known as magnetic flux. 

Practice Questions

1. When the coil is rotated between the pole pieces of a magnet as shown, how often will the magnetic flux linked with the coil be maximum and minimum during one complete rotation of the coil?

Ans: According to Faraday's law when the magnetic flux linking a circuit changes, an electromotive force is induced in the circuit proportional to the rate of change of the flux linkage.

So, when  rectangular coil is rotated in a uniform magnetic field about an axis passing through its centre and perpendicular to the direction of the field, then the induced voltage in the coil =dtdϕ​ ⇒ e.m.f= dϕ

⇒ e.m.f = NABωcosθ

where θ is the angle between the plane of the coil and the lines of force.

So, the induced emf in the coil is maximum when cosθ is maximum or θ is zero means when the plane of the coil is parallel to the field.

2. A rectangular loop has dimensions of 0.50m and 0.60m. The values of B are 0.02T and 45°, respectively. Calculate the magnetic flux at the surface.

Ans: Given:

Dimensions of rectangular loop = 0.50m and 0.60m,

B = 0.02T

θ = 45°

Magnetic flux formula is given by

ΦB = B A Cosθ

Area, A = 0.50 × 0.60

= 0.3 m2

ΦB = 0.02 × 0.3 × Cos 45

ΦB = 0.00312 Wb

3. A perpendicular field of force of magnitude 0.1 T is applied to an oblong loop with dimensions of three cm by 5 cm. How does one calculate the magnetic flux through the loop?

Ans: With formula ΦB = BACosθ, magnetic flux is defined because of the product of field, area, and therefore the angle between B and a unit vector perpendicular to the surface.

Here, the loop is positioned perpendicular to the force field B, namely the angle between B and a unit vector normal to the surface n is zero θ = 0⁰. Therefore, applying the formula we get,

=(0.1)(0.03×0.05)cos0∘

=15×10⁻⁻⁵

Wb =0.15 Wb

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