Magnetic Flux - Formula, SI Unit & CGS Unit
A sub-discipline of physics in the field of electromagnetism is the magnetic flux through a surface, which refers to the surface integral of the magnetic field's (B) normal component passing through that surface. To be specific, magnetic flux is defined as the number of magnetic field lines passing through a given closed surface. In this particular scenario, the area under consideration can be in any orientation corresponding to the direction of the magnetic field and of any size.
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Symbol and Formula of Magnetic Flux
Magnetic flux are denoted by the Greek letter Phi and have the symbol \[\Phi or \Phi _{B}\].
To calculate the magnetic flux, we can use the formula given below:
\[ \Phi _{B} = B. A = B A cos \Phi \]
Where,
\[ \Phi _{B} \] = Magnetic Flux
B = Magnetic Field
A = Area
\[ \Phi \] = Angle at which the magnetic field lines pass through the given surface area
Fluxmeter is used to measure the magnetic flux.
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SI Unit of Magnetic Flux
Weber (Wb) is the SI unit of magnetic flux, which is named after Wilhelm Eduard Weber, a German physicist. A flux density of one Weber per square meter or \[Wb/m^{2}\] is one Tesla, denoted by T (explained in the next section). Quite often, Weber is expressed in a multitude of other units, as shown below:
\[Wb = kg m^{2}/s^{2} A = V.s = H.A = T.m^{2} = J/A = 10^{8}Mx\]
Where, Wb = Weber, T = Tesla, V = volt, m = metre, J = joule, s = second, H = Henry, A = ampere, and Mx = Maxwell.
CGS unit of Magnetic Flux
The CGS unit of magnetic flux is Maxwell (Mx) or Abweber (abWb).
Fundamental Unit of Magnetic Flux
The fundamental unit of magnetic flux is Volt-seconds.
Understanding the Term Magnetic Flux Density
The force acting per unit length on a wire placed perpendicular (at right angles) to the magnetic field per unit current is the magnetic flux density (B).
Tesla (T) or \[ Kg s^{-2} A^{-1}\] is the SI unit of magnetic flux density (B).
The magnetic flux density, denoted by the symbol B, is a vector quantity
The CGS unit of magnetic flux density is Gauss, which is abbreviated as G or Gs
The formula for calculating the magnetic flux density is as follows:
B = F/I L
Where
F = total force acting on the wire
I = current flowing through the wire
L = length of the wire
Submultiples of Weber(Wb)
Multiples of Weber
Magnetic Flux
It can be defined as the total number of magnetic field lines which pass through a given closed surface. This quantity provides a measurement for the total magnetic field in a given area. The areas we take into consideration are of different sizes and different orientations considering the magnetic field direction. It is generally measured using a flux meter. There are different units for flux. In the SI unit, it is Weber which is abbreviated as Wb. The CGS unit that is used for this is Maxwell and the unit used fundamentally is Volt-Seconds. Thus, it is a measurement of the total magnetic field that passes through an area we take into consideration. It is a very good tool that can be used for finding the magnetic force on an area. It is related to the area chosen and we can choose an area of any size and arrange it according to the magnetic field.
Faraday conducted his experiment on electromagnetic induction and gave insights on the mathematical relation related to it. He made many contributions to science and was known greatly in the \[19^{th}\] century for his scientific contributions. Magnetic flux plays a major role in the process of electromagnetic induction. In order to calculate this quantity, we take into consideration the field-line image of a magnet or many magnets present.
FAQs on Magnetic Flux
1. What is meant by magnetic flux in Physics?
Magnetic flux is a measurement of the total number of magnetic field lines passing through a given surface. It quantifies the total magnetic field that penetrates an area. It is represented by the symbol Φ (Phi) and is a scalar quantity, although it is calculated from the magnetic field, which is a vector. The concept is crucial for understanding electromagnetic phenomena like induction.
2. How is magnetic flux calculated using its formula?
The magnetic flux (Φ) through a flat surface in a uniform magnetic field is calculated using the formula: Φ = B ⋅ A = BA cos(θ). In this formula:
- B is the magnitude of the magnetic field strength.
- A is the area of the surface.
- θ (theta) is the angle between the magnetic field lines and the normal (a line perpendicular) to the surface.
3. What is the SI unit and CGS unit of magnetic flux?
The SI unit of magnetic flux is the Weber (Wb), named after the German physicist Wilhelm Eduard Weber. One Weber is equivalent to one Tesla-meter squared (T·m²). The CGS (Centimetre-Gram-Second) unit for magnetic flux is the Maxwell (Mx).
4. How does magnetic flux differ from magnetic flux density?
Magnetic flux and magnetic flux density are related but distinct concepts:
- Magnetic Flux (Φ) is the total measure of magnetic field lines passing through a given surface. It represents the overall quantity of magnetism through an area. Its SI unit is the Weber (Wb).
- Magnetic Flux Density (B), also known as the magnetic field strength, is the amount of magnetic flux per unit area perpendicular to the direction of the flux. It measures the concentration or strength of the field at a point. Its SI unit is the Tesla (T).
Essentially, flux is the total effect, while flux density is the intensity.
5. Under what conditions is the magnetic flux through a surface maximum or minimum?
Based on the formula Φ = BA cos(θ), the magnetic flux depends on the orientation of the surface relative to the magnetic field:
- The flux is maximum when the surface is held perpendicular to the magnetic field lines. In this case, the angle θ between the field and the normal to the surface is 0°, and cos(0°) = 1, making Φ = BA.
- The flux is minimum (zero) when the surface is held parallel to the magnetic field lines. Here, the angle θ is 90°, and cos(90°) = 0, making Φ = 0.
6. What is the physical significance of zero magnetic flux through a closed surface?
The fact that the net magnetic flux through any closed surface is always zero is a fundamental principle known as Gauss's law for magnetism. It signifies that magnetic monopoles (isolated north or south poles) do not exist in nature. Since magnetic field lines always form closed loops, any field line that enters a closed surface must also exit it, resulting in a net flux of zero.
7. How is the concept of magnetic flux applied in an electric transformer?
The operation of an electric transformer is a direct application of changing magnetic flux. An alternating current in the primary coil creates a continuously changing magnetic field, which in turn produces a changing magnetic flux in the iron core. According to Faraday's Law of Induction, this changing flux induces an electromotive force (EMF) or voltage in the secondary coil, allowing for the stepping up or stepping down of voltage.
8. Can magnetic flux be negative, and what would it signify?
Yes, magnetic flux can be negative. The sign of the flux depends on the direction chosen for the surface normal vector (the vector perpendicular to the surface). By convention, if the magnetic field lines pass through the surface in the same direction as the normal vector, the flux is positive. If the field lines pass through in the opposite direction, the flux is considered negative. The negative sign simply indicates the direction of the flux relative to the defined orientation of the surface.
9. What is the dimensional formula for magnetic flux?
The dimensional formula for magnetic flux (Φ) is [ML²T⁻²A⁻¹]. This can be derived from its relationship with other physical quantities. For instance, from the formula for motional EMF (ε = Blv), we get B = ε / (lv). Since flux Φ = B⋅A, its dimensions are derived from EMF (voltage, [ML²T⁻³A⁻¹]), length ([L]), velocity ([LT⁻¹]), and area ([L²]).
