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👉 Chapter 5: Magnetism and Matter (Complete Notes)Chapter 6: Electromagnetic Induction
Vol 1: Magnetic Flux & Faraday's Laws
In previous chapters, we established that electric current produces a magnetic field. In this chapter, we explore the reverse phenomenon: Can a magnetic field produce electric current? This phenomenon is called Electromagnetic Induction (EMI).
1. Magnetic Flux ($\Phi_B$)
Magnetic Flux is defined as the number of magnetic field lines passing normally through a given surface area.
Unit: Weber (Wb) or Tesla-meter² ($Tm^2$)
Scalar Quantity
2. Faraday's Laws of Induction
- First Law: Whenever the magnetic flux linked with a closed circuit changes, an induced EMF (and hence induced current) is produced in it which lasts only so long as the change in flux continues.
- Second Law: The magnitude of the induced EMF is directly proportional to the time rate of change of magnetic flux.
(For a coil of N turns: $\varepsilon = -N \frac{d\Phi_B}{dt}$)
3. Lenz's Law
Statement: The polarity of induced EMF is such that it tends to produce a current which opposes the change in magnetic flux that produced it.
Vol 2: Motional EMF & Eddy Currents
1. Motional Electromotive Force
When a conductor moves in a magnetic field, the magnetic Lorentz force acts on its free electrons, creating a potential difference across its ends.
$$\varepsilon = Bvl$$
(Where $B, v, l$ are mutually perpendicular)
A rod of length $l$ rotating with angular velocity $\omega$:
$$\varepsilon = \frac{1}{2} B l^2 \omega$$
2. Eddy Currents
Eddy currents are loops of electrical current induced within bulk conductors by a changing magnetic field in the conductor according to Faraday's law of induction.
- Disadvantages: Unwanted heat generation in transformer cores and electric motors. Minimized by using Laminated Cores.
- Applications: Magnetic Braking in trains, Induction Furnaces, Electromagnetic Damping (Galvanometers).
Vol 3: Self & Mutual Inductance
1. Self Induction
Definition: The property of a coil by virtue of which it opposes any change in the strength of current flowing through it. It is often called Electrical Inertia.
Induced EMF: $\varepsilon = -L \frac{dI}{dt}$
Derivation: Self Inductance of a Long Solenoid
For a solenoid of length $l$, area $A$, and number of turns $N$:
$$L = \mu_0 n^2 Al = \frac{\mu_0 N^2 A}{l}$$
2. Mutual Induction
The phenomenon where a changing current in one coil (Primary) induces an EMF in a neighboring coil (Secondary).
Induced EMF: $\varepsilon_2 = -M \frac{dI_1}{dt}$
Derivation: Mutual Inductance of Two Coaxial Solenoids
$$M = \frac{\mu_0 N_1 N_2 A}{l}$$
(Assuming same length $l$ and Area $A$)
Coefficient of Coupling (K): Measure of how well two coils are magnetically linked. $M = K\sqrt{L_1 L_2}$.
Vol 4: Mission 100 Question Bank
Section A: MCQs
Q1. The SI unit of Magnetic Flux is:
(a) Tesla (b) Weber (c) Gauss (d) Henry
Ans: (b) Weber.
Q2. Lenz's law is a consequence of the law of conservation of:
(a) Charge (b) Momentum (c) Energy (d) Mass
Ans: (c) Energy.
Section B: Numericals (Important)
Q3. A 1.0 m long metal rod rotates about an axis passing through one end with an angular frequency of 400 rad/s in a perpendicular magnetic field of 0.5 T. Calculate the induced EMF.
Solution:
Given: $l = 1.0$ m, $\omega = 400$ rad/s, $B = 0.5$ T.
Formula: $\varepsilon = \frac{1}{2} B \omega l^2$
$\varepsilon = 0.5 \times 0.5 \times 400 \times (1)^2$
$\varepsilon = 0.25 \times 400 = 100$ V.
Ans: 100 Volts.
Q4. Current in a circuit falls from 5.0 A to 0.0 A in 0.1 s. If an average EMF of 200 V is induced, give an estimate of the self-inductance of the circuit.
Solution:
Formula: $|\varepsilon| = L \frac{dI}{dt}$
$200 = L \times \frac{5 - 0}{0.1}$
$200 = L \times 50 \Rightarrow L = 4$ H.
Ans: 4 Henry.
Section C: Conceptual
Q5. Why are the cores of transformers laminated?
Ans: To minimize energy loss due to Eddy Currents. Lamination increases resistance to the path of eddy currents.
Mission 100 Physics Series
Next Chapter: Alternating Current (AC) - The Powerhouse!
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