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

Summary

This video provides a clear and practical introduction to Faraday's Law of Electromagnetic Induction. Using coils of wire, an iron bar, and a voltmeter, it demonstrates how changing magnetic fields induce an electric current. The video explains that induced current occurs only when the magnetic flux changes, highlighting three ways to achieve this: altering the magnetic field, changing the coil's area, or rotating the coil relative to the field. A step-by-step example problem calculates induced emf, current, and power in a coil with multiple loops, emphasizing how more loops increase voltage. The content simplifies complex physics concepts for easy understanding and practical application.

Takeaways

• 🔋 Faraday's law of electromagnetic induction states that a change in magnetic flux induces an electromotive force (EMF) in a coil.
• 🌀 A steady current in a primary coil does not induce current in a secondary coil; only a changing current produces induction.
• ⚡ The induced EMF is calculated using the formula: emf = -n * (ΔΦ / Δt), where n is the number of loops, ΔΦ is the change in magnetic flux, and Δt is the time interval.
• 🌐 Magnetic flux (Φ) is determined by Φ = B * A * cos(θ), where B is the magnetic field, A is the coil area, and θ is the angle between the field and the normal to the coil.
• 🧲 One way to induce current is by changing the magnetic field, for example, by moving a magnet into or out of the coil.
• 🔄 Another method is to change the area of the coil, such as stretching or compressing it, while the magnetic field remains constant.
• 🔺 The third method is to change the angle between the magnetic field and the coil's normal line, which alters the magnetic flux.
• 📈 Increasing the number of loops in a coil amplifies the induced EMF proportionally.
• 💡 The current induced in a circuit can be calculated by dividing the induced EMF by the resistance (I = emf / R).
• 🔥 Power dissipated in a resistor due to induced current is given by P = I² * R, and can be significant if the EMF and current are large.
• ⏱️ Induced current only occurs during the period when the magnetic flux is changing, not when the field, area, or angle is constant.
• ⚖️ The negative sign in Faraday’s law reflects Lenz's Law, meaning the induced EMF opposes the change in magnetic flux.

Q & A

What is Faraday's law of electromagnetic induction?

Faraday's law states that a change in magnetic flux through a coil induces an electromotive force (EMF) in the coil. This induced EMF generates a current if the circuit is closed.

Why is no current induced when the current in the primary coil is steady?

A steady current produces a constant magnetic field, which does not change the magnetic flux through the secondary coil. Faraday's law requires a change in flux to induce EMF, so no current is induced.

What is the formula for calculating induced EMF according to Faraday's law?

The induced EMF is given by the formula: EMF = -N * (ΔΦ / Δt), where N is the number of loops, ΔΦ is the change in magnetic flux, and Δt is the change in time.

How is magnetic flux defined?

Magnetic flux (Φ) is defined as Φ = B * A * cosθ, where B is the magnetic field, A is the area of the coil, and θ is the angle between the magnetic field and the normal to the coil.

What are the three ways to induce an EMF in a coil?

An EMF can be induced by: 1) changing the magnetic field strength, 2) changing the area of the coil, and 3) changing the angle between the magnetic field and the coil.

How does moving a magnet into or out of a coil induce current?

Moving a magnet changes the magnetic field through the coil, which changes the magnetic flux. According to Faraday's law, this change in flux induces an EMF and generates a current in the coil.

How does changing the area of a coil affect magnetic flux?

Increasing or decreasing the area of the coil changes the amount of magnetic field passing through it, thus changing the magnetic flux and inducing an EMF in the coil.

How does rotating a coil in a magnetic field induce EMF?

Rotating the coil changes the angle θ between the magnetic field and the normal to the coil. Since flux depends on cosθ, changing the angle changes the flux, which induces an EMF.

In the example problem, how is the induced EMF calculated for a square coil with changing magnetic field?

The induced EMF is calculated using EMF = -N * (ΔB * A * cosθ / Δt). With N = 50 loops, ΔB = 8 T, area A = 0.04 m², θ = 0°, and Δt = 0.1 s, the EMF is -160 V in magnitude.

How is the current through a resistor connected to the coil calculated?

The current is calculated using Ohm's law: I = EMF / R. In the example, EMF = 160 V and R = 20 Ω, so the current I = 160 / 20 = 8 A.

How is the power dissipated by the resistor calculated?

The power is calculated using P = I² * R. With I = 8 A and R = 20 Ω, the power P = 8² * 20 = 1280 W.

Why does increasing the number of loops in a coil increase the induced EMF?

The induced EMF is directly proportional to the number of loops (N) in the coil. More loops mean each loop contributes to the total EMF, increasing the overall voltage generated.