Summary of "PY212 Video 23C Faradays Law - Changing A"

Summary of “PY212 Video 23C Faraday’s Law - Changing A”

This video focuses on applying Faraday’s Law of Induction specifically to situations where the area of a coil or loop changes in a magnetic field, rather than the magnetic field itself changing. It also introduces the concept of motional EMF, which arises when a conductor moves through a magnetic field.

Main Ideas and Concepts

Faraday’s Law Recap

Faraday’s law relates the induced electromotive force (EMF) in a coil to the rate of change of magnetic flux through it.
Magnetic flux (Φ) is given by: [ \Phi = B \cdot A \cdot \cos\theta ] where:
- ( B ) = magnetic field strength,
- ( A ) = area of the coil,
- ( \theta ) = angle between the magnetic field and the normal to the coil.

Changing Area in a Magnetic Field

Unlike previous cases where the magnetic field ( B ) changes, this video focuses on changing the coil’s area ( A ).
When the area decreases or increases, the magnetic flux changes, inducing an EMF according to Faraday’s law.

Lenz’s Law Application

The direction of the induced EMF and current opposes the change in magnetic flux.
Steps to find direction:
1. Identify external magnetic field direction.
2. Determine if area (and thus flux) is increasing or decreasing.
3. Induced magnetic field direction opposes the flux change.
4. Use right-hand rule to find induced current and EMF direction.

Example 1: Coil Area Decreasing

A 50-turn coil’s area decreases from 0.5 m² to 0.1 m² in 0.2 seconds inside a constant magnetic field.
Induced EMF magnitude calculated using: [ \text{EMF} = N B \cos\theta \frac{\Delta A}{\Delta t} ]
Direction determined using Lenz’s law and right-hand rule.
Result: 20 volts induced EMF.

Example 2: Sliding Metal Bar on Rails

A sliding metal bar moves along metal rails in a magnetic field, changing the loop area.
Area increases as the bar slides, increasing flux.
Induced magnetic field opposes the external field.
Induced current direction found via right-hand rule.
EMF calculated using Faraday’s law with ( N=1 ).

Derivation of a Special Equation for Sliding Bar Apparatus

Area ( A = L \times X ), where ( L ) is fixed length, ( X ) changes with bar position.
EMF equation becomes: [ \text{EMF} = B L v \sin\theta ] where:
- ( B ) = magnetic field strength,
- ( L ) = length of the bar,
- ( v = \frac{\Delta X}{\Delta t} ) = speed of the bar,
- ( \theta ) = angle between velocity vector ( v ) and magnetic field ( B ).
This formula is specific to this apparatus but has broader applications.

Motional EMF

When a conductor moves through a magnetic field, electrons experience a magnetic force pushing them to one side, causing charge separation.
This creates an electric field opposing the magnetic force.
At equilibrium, electric force equals magnetic force: [ qE = qvB \sin\theta \implies E = vB \sin\theta ]
Potential difference (motional EMF) across the conductor: [ \text{EMF} = E L = B L v \sin\theta ]
Motional EMF is the voltage induced by physical motion of a conductor in a magnetic field.
Examples include waving a screwdriver through Earth’s magnetic field or voltage across an airplane wing in flight.

Connection Between Sliding Bar and Motional EMF

The sliding bar apparatus is a practical example of motional EMF.
The derived equations are the same because the sliding bar is effectively a conductor moving through a magnetic field.

Methodology / Steps to Solve Changing Area Problems with Faraday’s Law

Identify the external magnetic field ( B ) and its direction.
Determine how the area ( A ) of the coil or loop is changing (increasing or decreasing).
Apply Lenz’s law:
- If flux is decreasing, induced magnetic field is in the same direction as external ( B ).
- If flux is increasing, induced magnetic field is opposite to external ( B ).
Use right-hand rule to find the direction of the induced current and EMF.
Calculate the magnitude of induced EMF using: [ \text{EMF} = N B \cos\theta \frac{\Delta A}{\Delta t} ]
For sliding bar apparatus or moving conductor, use the motional EMF formula: [ \text{EMF} = B L v \sin\theta ] where ( v ) is velocity of the conductor, ( L ) its length, and ( \theta ) the angle between ( v ) and ( B ).

Speakers / Sources Featured

Primary Speaker: The instructor or lecturer presenting the PY212 physics course content on Faraday’s law.
No other speakers or external sources are mentioned or featured in the video.

This summary captures the main ideas, conceptual explanations, example problems, and derived formulas related to Faraday’s law with changing area and motional EMF from the video.