Edexcel A Level (IAL) Physics-4.25 Magnetic Flux Density, Flux & Flux Linkage- Study Notes- New Syllabus
Edexcel A Level (IAL) Physics -4.25 Magnetic Flux Density, Flux & Flux Linkage- Study Notes- New syllabus
Edexcel A Level (IAL) Physics -4.25 Magnetic Flux Density, Flux & Flux Linkage- Study Notes -Edexcel A level Physics – per latest Syllabus.
Key Concepts:
- understand and use the terms magnetic flux density \(B\), flux \(\phi\) and flux linkage \(N\phi\)
Magnetic Flux Density, Magnetic Flux and Flux Linkage
Magnetic effects are described using the related quantities magnetic flux density, magnetic flux, and flux linkage. These quantities are essential for understanding electromagnetic induction.
Magnetic Flux Density \( B \)
Magnetic flux density describes the strength of a magnetic field at a point.
Definition: Magnetic flux density is defined as the force per unit current per unit length on a conductor placed at right angles to the magnetic field.
\( B = \dfrac{F}{IL} \)
- \( B \) = magnetic flux density (tesla, T)
- \( F \) = force on the conductor (N)
- \( I \) = current in the conductor (A)
- \( L \) = length of conductor in the field (m)
Meaning:
- Larger \( B \) means a stronger magnetic field.
- 1 tesla is a very strong magnetic field.
Magnetic Flux \( \phi \)
Magnetic flux represents the total magnetic field passing through a given area.
Definition:
\( \phi = BA \)
(for a uniform magnetic field perpendicular to the area)
- \( \phi \) = magnetic flux (weber, Wb)
- \( B \) = magnetic flux density (T)
- \( A \) = area (m²)
If the field is at an angle \( \theta \) to the normal of the area:
\( \phi = BA\cos\theta \)
Key points:
- Flux is maximum when the field is perpendicular to the area.
- Flux is zero when the field is parallel to the area.
Flux Linkage \( N\phi \)
Flux linkage accounts for the total magnetic flux linked with a coil of wire.
Definition:
\( \text{Flux linkage} = N\phi \)
- \( N \) = number of turns in the coil
- \( \phi \) = magnetic flux through one turn (Wb)
Meaning:
- Increasing the number of turns increases the flux linkage.
- Flux linkage is central to Faraday’s law of electromagnetic induction.
Units Summary
| Quantity | Symbol | SI Unit |
|---|---|---|
| Magnetic flux density | \( B \) | tesla (T) |
| Magnetic flux | \( \phi \) | weber (Wb) |
| Flux linkage | \( N\phi \) | weber-turns (Wb) |
Importance in Electromagnetic Induction
- A changing magnetic flux produces an induced e.m.f.
- It is the rate of change of flux linkage that matters.
- This leads directly to Faraday’s law.
Example (Easy)
A uniform magnetic field of flux density \( 0.20\ \mathrm{T} \) passes perpendicularly through a coil of area \( 0.050\ \mathrm{m^2} \). Calculate the magnetic flux.
▶️ Answer / Explanation
\( \phi = BA = 0.20 \times 0.050 = 0.010\ \mathrm{Wb} \)
Example (Medium)
A coil of 200 turns experiences a magnetic flux of \( 3.0\times10^{-4}\ \mathrm{Wb} \) per turn. Find the flux linkage.
▶️ Answer / Explanation
\( N\phi = 200 \times 3.0\times10^{-4} = 0.060\ \mathrm{Wb} \)
Example (Hard)
A square coil of side \( 0.10\ \mathrm{m} \) is placed in a uniform magnetic field of flux density \( 0.50\ \mathrm{T} \). The field is at \( 60^\circ \) to the normal of the coil. Calculate the magnetic flux through the coil.
▶️ Answer / Explanation
Area of coil:
\( A = 0.10^2 = 0.010\ \mathrm{m^2} \)
Magnetic flux:
\( \phi = BA\cos\theta = 0.50 \times 0.010 \times \cos 60^\circ = 2.5\times10^{-3}\ \mathrm{Wb} \)