Summary of "Faraday's Law of Electromagnetic Induction, Magnetic Flux & Induced EMF - Physics & Electromagnetism"

Summary of the Video

Faraday’s Law of Electromagnetic Induction, Magnetic Flux & Induced EMF - Physics & Electromagnetism

Main Ideas and Concepts

Introduction to Faraday’s Law of Electromagnetic Induction

When a coil of wire is placed near another coil connected to a battery and resistor, no current is induced in the second coil if the current in the first coil is steady.
An induced emf (and thus current) appears only when the current in the first coil changes (i.e., when the switch is closed or opened briefly).
This phenomenon is the basis of Faraday’s law: a change in magnetic flux induces an emf in a coil.

Faraday’s Law Formula

[ \text{Induced emf} = -N \frac{\Delta \Phi}{\Delta t} ]

where: - (N) = number of loops in the coil - (\Delta \Phi) = change in magnetic flux - (\Delta t) = change in time

The negative sign represents Lenz’s law, indicating that the direction of the induced emf opposes the change in flux.

Magnetic Flux ((\Phi)) Definition

[ \Phi = B \times A \times \cos \theta ]

where: - (B) = magnetic field strength - (A) = area of the coil - (\theta) = angle between the magnetic field and the normal (perpendicular) to the coil’s surface

Three Ways to Change Magnetic Flux and Induce EMF

Change the Magnetic Field ((B))
- Example: Moving a magnet into or out of a coil changes the magnetic field through the coil, inducing emf.
- If the magnet is stationary, no emf is induced because flux is constant.
Change the Area ((A)) of the Coil
- Example: Stretching or compressing a coil changes its area, altering the flux.
Change the Angle ((\theta)) Between Magnetic Field and Coil
- Example: Rotating the coil changes the angle between the magnetic field and the coil’s normal line, changing the flux.

Practical Example / Problem Solving

Given a square coil with 50 loops, dimensions 0.2 m × 0.2 m, and a magnetic field increasing from -3 T to 5 T perpendicular to the coil face.
Calculate induced emf, current through a resistor, and power dissipated.

Step-by-step Problem Solution

Given

Number of loops, (N = 50)
Side length of square coil = 0.2 m
Magnetic field change, (\Delta B = 5 - (-3) = 8\, T)
Area, (A = 0.2 \times 0.2 = 0.04\, m^2)
Angle, (\theta = 0^\circ) (cos 0° = 1)
Time interval, (\Delta t = 0.1\, s)
Resistance, (R = 20\, \Omega)

Calculate Induced EMF

[ \text{emf} = -N \frac{\Delta \Phi}{\Delta t} = -50 \times \frac{8 \times 0.04 \times 1}{0.1} = -160\, V ]

(Negative sign ignored for magnitude.)

Calculate Current

[ I = \frac{\text{emf}}{R} = \frac{160}{20} = 8\, A ]

Calculate Power Dissipated in Resistor

[ P = I^2 R = 8^2 \times 20 = 64 \times 20 = 1280\, W ]

Additional Insight

More loops increase the induced emf proportionally.
A single loop would produce only ( \frac{160}{50} = 3.2\, V ).

Key Takeaways

Faraday’s law explains how changing magnetic flux induces emf and current in a coil.
Magnetic flux depends on magnetic field strength, coil area, and angle between field and coil.
Induced emf can be generated by changing any of these three factors.
The magnitude of induced emf is proportional to the number of loops in the coil.
Practical calculations involve applying Faraday’s law formula and Ohm’s law to find current and power.