Test: Magnetic Flux (20 Dec) - JEE MCQ

When an iron rod is inserted inside a solenoid the magnetic field inside the solenoid increases due to the high magnetic permeability of iron. Due to the increased magnetic field, the magnetic flux also increases. The self-inductance of the solenoid also increases because self-inductance (L) of the coil is directly proportional to the permeability of the material inside the solenoid. The rate of joule heating doesn’t change.

The induced emf ,E=− dϕ​/dt where ϕ=magnetic flux
Hence, emf will last as long as flux keeps changing.

Magnetic Flux Formula
Magnetic flux is the product of the average magnetic field times the perpendicular area that it crosses.
Magnetic flux = number of turns x Magnetic field x Area x (angle between the planar area and the magnetic flux)
The equation is:
Φ =N B A cos(θ)
Where:
N=number of turns
Φ: Magnetic Flux
A: Area
B: Magnetic field
θ: angle between a perpendicular vector to the area and the magnetic field

When a magnet is moved towards the coil quickly, the rate of change of flux is larger than that if the magnetic field is moved slowly, thus larger emf is induced due to quick movement of the coil.

A cylindrical bar magnet is kept along the axis of a circular coil. If the magnet is rotated about its axis, then there is no change in magnetic flux, there is no emf induced in the coil, no current will be induced in the coil.

Explanation of the relationship between magnetic flux and number of turns:
 

• Definition of magnetic flux: Magnetic flux is the measure of the total magnetic field passing through a given area. It is represented by the symbol Φ.


• Formula for magnetic flux: The formula for magnetic flux is given by Φ = B * A * cos(θ), where B is the magnetic field strength, A is the area through which the magnetic field passes, and θ is the angle between the magnetic field and the normal to the area.


• Relationship with number of turns: The magnetic flux linked with a coil is directly proportional to the number of turns of the coil. This means that as the number of turns in the coil increases, the magnetic flux linked with the coil also increases.


• Mathematical representation: Mathematically, this relationship can be expressed as Φ ∝ N, where Φ is the magnetic flux and N is the number of turns of the coil.


• Explanation: When the number of turns in a coil is increased, the total area through which the magnetic field passes also increases. This results in a larger magnetic flux being linked with the coil. Therefore, the magnetic flux linked with a coil is directly proportional to the number of turns of the coil.


 

The measurement of the total magnetic field that passes through a given area is known as magnetic flux. It is helpful in describing the effects of the magnetic force on something occupying a given area.
If we consider a simple flat area A as our example and angle θ as the angle between the normal to the surface and a magnetic field vector, then the magnetic flux is given by the equation:
ϕ=BAcosΘ
 

 The total flux is given by φ = ∫ B.ds, where ∫ds is the area. Thus φ = BA. We get φ = 11.7 x 2 = 23.4 units.