Open In App

Magnetic Flux

Improve
Improve
Like Article
Like
Save
Share
Report

Magnetic Flux is defined as the surface integral of the normal component of the Magnetic Field(B) propagating through that surface. It is indicated by φ or φB. Its SI unit is Weber(Wb). The study of Magnetic Flux is done in Electromagnetism which is a branch of physics that deals with the relation between Electric Current and Magnetic Field

In this article, we will learn about Magnetic Flux in detail and also learn about laws related to it.

Magnetic Flux Definition

Magnetic Flux is defined as,

The number of Magnetic Field lines flowing through a closed surface is known as Magnetic Flux. It calculates the total magnetic field that travels across a specific surface area.

The region under consideration might be any size and can be oriented in any direction about the magnetic field direction. 

Magnetic Flux Symbol

The Greek letter Phi or the Phi suffix B is often used to represent Magnetic Flux. The symbol for Magnetic Flux is ϕ or ϕB.

Magnetic Flux Formula

Magnetic Flux Formula is given as:

ϕB = B.A = B A cosθ

where

  • A is the Surface Area
  • B is the Magnetic Field
  • θ is the Angle at which lines pass through the Area
  • ϕB is the Magnetic Flux

Understanding Magnetic Flux

The development of the concept of Magnetic Flux is attributed to Michael Faraday. Faraday’s breakthrough came when he discovered a simple mathematical relationship to explain a series of electromagnetic induction tests he did. Faraday is largely regarded as the greatest experimental scientist of the nineteenth century, having made significant advances to science. Before we begin to appreciate his work, we must first comprehend the idea of magnetic flux, which is critical to electromagnetic induction.

We use the Field-Line picture of a Magnet or a set of magnets to compute the Magnetic Flux. The scalar product of the magnetic field and area ‘A’ gives the Magnetic Flux through a plane of area ‘A’ that is put in a Uniform Magnetic Field of magnitude B. It’s also necessary to consider the angle at which the field lines travel across the given surface area.

Magnetic Flux

Mathematically,

ϕB = B.A = B A cosθ

where, θ is the angle between vectors A and B.

The resultant flux depends on the glancing angle in the following manner:

  • When the angle is 90°, the flux is lowest as Cos 90° is zero.
  • When the angle is 0°, the flux is largest as Cos 0° is 1.

Calculation of Total Magnetic Flux

If the Magnetic Field is non-uniform, with various magnitudes and directions at different areas of the surface, the total magnetic flux across the surface may be calculated as the product of all such area elements and their respective magnetic fields.

Mathematically,

ϕB = B1.dA1 + B2.dA2 + B3.dA3 + … = ∑all Bi.dAi

Magnetic Flux is Vetor or Scalar

The Magnetic Flux is a Scalar quantity, as shown by the equation above. Weber (Wb) or Tesla Meter Squared is its SI unit (Tm2).

Measurement of Magnetic Flux

A Magnetometer may be used to measure the Magnetic Flux. Assume a magnetometer probe is moved over a 0.9 m2 region near a huge sheet of magnetic material and shows a constant reading of 10 mT. The magnetic flux through that area is then computed using the formula (10 × 10−3 T) (0.9 m2) = 0.0090 Wb. It would be essential to find the average measurement in the event of shifting magnetic field readings across a large region. The Weber (Wb) or Tesla Meter Squared (Tm2) unit of Magnetic Flux is named after German scientist Wilhelm Weber.

Magnetic Flux  Unit

A Flux Meter is used to measure the Magnetic Flux. The following are the SI and CGS units of Magnetic Flux:

  • Weber (Wb) is the SI unit for Magnetic Flux.
  • Volt-Seconds is the fundamental unit of Magnetic Flux
  • Maxwell is the CGS unit of Magnetic Flux

Gauss Law of Magnetism

Gauss’s Law of Magnetism states that the net magnetic flux through any closed surface is zero. Let’s say Magnetic Flux through an elemental area ΔA is given by  ΔφB = B. ΔA then net Magnetic Flux is given as 

φB = ∫ΔφB = ∫B. ΔA = 0

It means that the total number of magnetic field lines entering the surface is equal to the total number of lines exiting the surface.

Physical Significance of Gauss Law of Magnetism

The physical significance of Gauss law is that there is no source or sink of magnetic field lines, and isolated magnetic monopoles don’t exist i.e. even the smallest magnetic element consists of a dipole or a current loop.

Magnetic Flux Density

The force operating per unit current per unit length on a wire positioned perpendicular to the magnetic field is called Magnetic Flux Density(B). In simple terms, it is the Magnetic Flux per unit area positioned perpendicular to the Magnetic Flux. Magnetic Flux Density is a Vector Quantity. It is represented by B.

Magnetic Flux Density Formula

Magnetic Flux Density Formula is given as:

B = F ⁄ I L

where,

  • I is the current flowing through the wire
  • L is the length of wire
  • F is the total force acting on the wire

Magnetic Flux Density Unit

The Unit of Magnetic Flux Density is

  • Tesla (T) or Kg s−2 A−1 is the SI unit of Magnetic Flux Density
  • Gauss is the CGS Unit of Magnetic Flux Density

Read More,

FAQs on Magnetic Flux

Q1: What is Magnetic Flux?

Answer:

Magnetic Flux is defined as the number of Magnetic Field lines passing through a closed surface. It is the surface integral of the normal component of the Magnetic Field propagating through that surface.

Q2: What is Magnetic Field?

Answer:

Magnetic Field is the region around a magnet in which it exerts force on another magnetic object. The strength of magnetic field decreases as we go away from the magnet.

Q3: How is Magnetic Field Produced?

Answer:

When a charged particle move it produces magnetic field around it.

Q4: What is the Formula for Magnetic Field Density?

Answer:

Formula of Magnetic Field Density is given by B = F ⁄ I L.

Q5: What is the Basic Source of the Magnetic Field?

Answer:

A moving electric charge is the basic source of the Magnetic Field.

Q6: Why Magnetic Field lines are Closed Curves?

Answer:

Since, as per Gauss Law of Magnetism, Magnetic MonoPole doesn’t exist hence magnetic field lines originate from one pole and enter other making closed curves.

Q7: Why Magnetic Field Lines never intersect?

Answer:

The direction of the Magnetic Field at a point is given by tangent to the Magnetic Field lines. If they intersect then there will be two tangents indicating two directions which is not possible hence Magnetic filed lines never intersect.



Last Updated : 04 Feb, 2024
Like Article
Save Article
Previous
Next
Share your thoughts in the comments
Similar Reads