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Magnetic flux formula is denoted by ΦB, where B is a magnetic field and its unit is Weber (Wb). The magnetic flux is a measure of the total magnetic field that flows across a specific location and it is a vector quantity. It is a valuable tool for describing the effects of the magnetic force on things in a specific location. The magnetic flux measurement is specific to the area specified and is calculated by multiplying the average magnetic field by the perpendicular area it traverses. Let’s discuss this in detail along with some important questions.
Check also: NCERT Solutions For Class 12 Physics Chapter 6- Electromagnetic Induction
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Key Takeaways: Magnetic flux, magnetic flux formula, magnetic field, magnetic force, magnetic flux density, Weber, Vector, Surface
Magnetic Flux Formula
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Magnetic flux is represented by the symbol ØB, where B represents a magnetic field and the unit is Weber (Wb). The magnetic flux rate is a vector quantity that relies on the direction of the magnetic field. The magnetic flux formula is:
\(\Phi_B = B.A\)
\(\Phi_B = B.ACos \theta\)
Where,
B stands for the magnetic field.
A = area of the surface and
Θ= The angle formed by the magnetic field and the normal to the surface.
Read more: Electromagnetic Induction MCQ
Magnetic Flux Density
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Magnetic Flux Density is the quantity of magnetic flux passing through a unit area perpendicular to the direction of the magnetic flux. By B=H, Flux Density (B) is connected to Magnetic Field (H). It is expressed in Webers per square meter, which is equivalent to Tesla [T].
OR,
Magnetic flux density is a vector field with SI units of tesla that we denote with the sign B. (T). While providing a formal definition, examine the wider idea of the magnetic field. The tesla is the International System (SI) unit of field "magnetic flux density" (T). The magnetism of one tesla is rather powerful.
Example of Magnetic Flux
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The input to magnetic flux for a particular area is equal to the area multiplied by the magnetic field component perpendicular to the region. The total magnetic flux on a closed surface is always equal to zero (Gauss' law of magnetism). No matter how tiny the volume, magnetic forces are always dipole sources (similar to micro bar magnets), with as many magnetic field lines pouring in (to the south pole) as out (from the north pole).
Example of Magnetic Flux
Read more: Electromagnetic Induction and Alternating Currents Important Questions
Measurement of Magnetic Flux
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The Si-derived unit of magnetic flux is the Weber (named after the German physicist and founder of the telegraph Wilhelm Weber), and the sign is Wb. Since magnetic flux is just an expression of the magnetic field in a specific location, it can be detected with a magnetometer in the same way that the magnetic field can.
Assume a tiny magnetometer probe is moved about (without spinning) inside a 0.5m2 region near a big sheet of magnetic material and returns a consistent reading of 5Mt. (5.10-3 T).(0.5 m2) = 0.0025 Wb denotes the magnetic flux through the location. In the event that the magnetic field reading varies with position, the average reading must be determined.
The magnetic flux density is a related word that you may stumble across. This is expressed in Wb/m2. We could easily declare the units of flux density in Tesla since we are dividing flux by area. In reality, the terms magnetic flux density and magnetic field magnitude are frequently used interchangeably.
Also Check: Induced Electromotive Force and Current
Magnetic Flux Through Open and Closed Surfaces
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One of the four Maxwell's equations, Gauss's law for magnetism, asserts that the net magnetic flux across a closed surface equal zero. (A "closed surface" is one that entirely encloses a volume(s) and contains no holes.) This law arises from the empirical fact that magnetic dipoles have never been discovered. It can be written in form of equation:
\(\Phi_B = \oint \oint_S B.dS=0\)
While magnetic flux via a closed surface is always zero, magnetic flux across an open surface does not have to be and is an essential number in electromagnetism. When calculating the total magnetic flux across a surface, only the surface's border must be defined; the exact shape of the surface is immaterial, and the sum over any surface with the identical boundary will be identical. This is due to the fact that the closed surface flux is zero.
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Why is Magnetic Flux Useful
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When a wire coil is moved throughout a magnetic field, a voltage is formed that is proportional to the magnetic flux passing through the coil's area. Faraday's law describes this. Electric engines and generators use Faraday's law to rotate coils in a magnetic field.
The flux in this example fluctuates as the coil turns. Even when the magnetic field is intricate, engineers may readily compute the voltage produced by an electric generator using the magnetic flux formulation.
Uses of Magnetic Flux
In reality, we can utilise a closed surface that completely covers a region of interest, such as a sphere. Since Gauss' rule of magnetism, closed surfaces are of great interest to physicists. Since magnets always have two poles, there is no prospect of a magnetic monopole within a closed surface.
This indicates that the overall magnetic flux via such a closed surface is always zero, and all magnetic field lines entering the closed surface are perfectly balanced by field lines exiting the closed surface. This information can help to simplify magnetic field difficulties.
Read more: Unit of Magnetic Flux
Things to Remember
- An electromotive force is caused by a change in the magnetic field flux (or voltage).
- The magnetic flux (commonly abbreviated Φ or Φ B) travelling through a surface is a component of the magnetic field that passes through that surface.
- Magnetic flux is defined in its most generic form as \(\Phi_B = \oint \oint_A B.dA\). It is the integral (sum) of all magnetic fields travelling through elements of microscopic area dA.
- region of the vector: A vector with the same magnitude as the area under consideration and the same direction as the surface area.
- A galvanometer is an analogue measuring instrument, represented by the letter G, that measures current flow by measuring the deflection of a needle generated by a magnetic field force acting on a current-carrying wire.
Read More: Solenoid Engine
Previous Year Questions
Questions on Lenz Law :
- Lenz’s law is consequence of the law of conservation of….. [UPSEE 2019]
- The magnetic field is increasing at a constant rate. The directions of induced current in wires AB and CD are…. [VITEEE 2019]
- the circular loop of wire is moved with velocity towards the infinite current carrying wire…… [VITEEE 2016]
- Two identical coaxial coils P and Q carrying equal amount of current in the same direction are brought nearer. The current in...[KEAM]
- The polarity of induced emf is given by….[KEAM]
Questions on Electromagnetic Induction:
- If a transformer of an audio amplifier has output impedance 8000 0 and the speaker has input impedance…...[JCECE 2005]
- A conducting loop in the shape of a right angled isosceles triangle of height 10cm10cm is kept such that the 90∘ vertex is…..[JEE Advance 2016]
- A 10m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0ms−1……. [ JEE Main 2019]
- If a current of 2.0A2.0A flows through the smaller loop, then the flux linked with bigger loop is…… [JEE Main 2013]
- A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B….. [JEE Main 21018]
- A copper rod of mass m slides under gravity on two smooth parallel rails, with separation ll and set at an angle of θ with the horizontal….. [JEE Main 2018]
- A copper wire is wound on a wooden frame, whose shape is that of an equilateral…. [JEE Main 2019]
- A metallic rod of length ll is tied to a string of length 2l and made to rotate with angular speed…. [JEE Main 2013]
- A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plane of the paper…. [JEE Main 2014]
- If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is… [JEE Main 2019]
- Figure shows a circular area of radius R where a uniform magnetic field….
- In a coil of resistance 100Ω , a current is induced by changing the magnetic flux through it….. [JEE Main 2017]
- When current in a coil changes from 5A to 2A…. [JEE Main 2015]
Questions on Faradays laws of induction:
- Two identical circular coils A and B are kept on a horizontal tube side by side without touching each other…. [KCET 2013]
- The magnetic flux through a circuit of resistance RR changes by an amount….[NEET 2004]
- A conducting loop in the shape of a right angled isosceles triangle of height...[JEE Advance 2016]
- If a transformer of an audio amplifier has output impedance…..[JCECE]
Sample Questions
Ques: What is Faraday's contribution to Magnetic flux? (2 Marks)
Ans: Faraday's profound discoveries stemmed from his discovery of a simple mathematical relationship to explain a series of experiments he did on electromagnetic induction. Faraday made several advances to science and is largely regarded as the nineteenth century's finest experimental scientist.
Ques: How do we Understand Magnetic flux? (4 Marks)
Ans: To compute the magnetic flux, we use the field-line picture of a magnet or a set of magnets. As the scalar product of the magnetic field and the area A, the magnetic flux across a plane of area A placed in a homogeneous magnetic field of magnitude B is provided.
The angle where the field lines travel across the given surface area is also significant in this case. The resultant flux is relatively low if the field lines contact the area at a glancing angle, that is, when the angle between the magnetic field vector and the area vector is almost equal to 90o. The resultant flux is greatest when the angle is equal to 0 Degree.
Ques: A circular antenna with a surface size of 3 m2 has been built in Madurai. The plane of the antenna's region is slanted at 47o with respect to the direction of the Geomagnetic field. Calculate the magnetic flux associated with the antenna if the strength of the Earth's field at that location is 40773.9 nT. (2 Marks)
Ans: B = 40773.9 nT; θ = 90º – 47º = 43°;
A = 3m2
Also, ΦB = BAcosθ
Ques. When a current-carrying wire is put in a magnetic field, what devices act on torque? (2 Marks)
Ans: The devices are as follows:
- Galvanometer
- Ammeter
- Voltmeter
Ques. What is the worth of one weber? (3 Marks)
Ans: Faraday's law, which connects a change in the magnetic flux through a loop to the electric field all around loop, may be used to describe the weber. A one-weber-per-second shift in flux results in a one-volt electromagnetic force (Generates an electric possible difference of one volt around two open-circuited terminals).
Official explanation: Weber (magnetic flux unit) — The weber is the magnetic field that, if it were lowered to zero at a consistent speed of one second, would create an electromotive of one volt in a one-turn circuit.
Ques. When is the magnetic flux at its peak? (4 Marks)
Ans: When the magnetic flux across a coil is equal to zero, it is at its maximum. As a result, equal this equation to zero and calculate the angle between both the coil's plane and the planes of force.
Magnetic flux through a material is greatest when the magnetic field's direction coincides with the material's normal vector. In other sense, when the magnetic field is parallel to the surface area, the magnetic flux is greatest. This is why φ=BAcos, where is the angle between both the magnetic field direction and the usual vector of the surface area. When the magnetic field is perfectly parallel to the normal vector (i.e. perpendicular to the surface) ,θ=0 and cos = 1, its highest value.
Ques: Magnetic Flux has a Direction. Explain. (4 Marks)
Ans: The magnetic field is stronger towards the magnet's poles, where the flux lines are more packed tightly. Magnetic flux flows in a broad direction from the North (N) pole to the South (S). Furthermore, these magnetic lines create complete loops that exit at the north pole and enter at the south pole of the magnet. Magnetic poles have always been found in groups of two.
Magnetic flux, on the other hand, does not truly move from the north to the south pole, or anywhere else for that matter, because magnetic flux is a static zone around a magnet in which the magnetic force persists. In other terms, magnetic flux does not flow or move; it just exists and is unaffected by gravity.
Ques. What are the importance points while plotting Lines of Force in Magnetic Flux? (4 Marks)
Ans: When graphing lines of force, certain key facts emerge:
- Force lines are NEVER crossed.
- Force lines are CONTINUOUS.
- Single CLOSED LOOPS of force always develop around the magnet.
- Lines of force have a certain DIRECTION that runs from north to south.
- Closely spaced force lines imply a STRONG magnetic field.
- Force lines that are farther apart suggest a WEAK magnetic field.
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