Comprehensive NEET Physics Notes: Electromagnetic Induction and Alternating Current

1. Electromagnetic Induction

1.1 Faraday's Law of Induction

Faraday's law states that the electromotive force (emf) induced in a circuit is directly proportional to the rate of change of magnetic flux through the circuit. Mathematically, it is given by:

$ϵ=-\frac{d{\Phi }_B}{dt}$

Where:

• $ϵ$ is the induced emf
• ${\Phi }_B$ is the magnetic flux

The negative sign indicates that the induced emf generates a current that opposes the change in magnetic flux, as described by Lenz's law.

NEET Tip:

Remember that the induced emf is only present when there is a change in magnetic flux. If the magnetic flux is constant, no emf is induced.

1.2 Lenz's Law

Lenz’s law provides the direction of the induced current: the induced current will flow in such a direction that it will oppose the change in the magnetic flux that produced it. This is a direct consequence of the conservation of energy.

Example Application:

• Consider a loop of wire near a magnet. If the magnet is moved towards the loop, the induced current will create a magnetic field opposing the motion of the magnet. Conversely, if the magnet is moved away, the induced current will create a magnetic field that tries to keep the magnet close.

Common Mistake:

Students often forget the negative sign in Faraday's law, leading to incorrect predictions of the direction of the induced current.

1.3 Magnetic Flux

Magnetic flux through a surface of area $A$ in a magnetic field $B$ is given by:

${\Phi }_B=B\cdot A\cdot \cos \theta$

Where:

• $A$ is the magnetic field
• $A$ is the area vector
• $\theta$ is the angle between the magnetic field and the normal to the surface

Did You Know?

The SI unit of magnetic flux is the weber (Wb), where 1 Wb = 1 Tm².

2. Alternating Current

2.1 AC Generator

An AC generator works on the principle of electromagnetic induction. It converts mechanical energy into electrical energy by rotating a coil in a magnetic field. The emf generated is sinusoidal and is given by:

$ϵ={ϵ}_0\sin (\omega t)$

Where:

• ${ϵ}_0=NBA\omega$ is the peak emf
• $N$ is the number of turns in the coil
• $B$ is the magnetic field
• $A$ is the area of the coil
• $\omega$ is the angular velocity

2.2 RMS Values

The root mean square (RMS) value of an alternating current or voltage is the effective value that represents the DC equivalent. For a sinusoidal waveform:

$I_{rms}=\frac{I_0}{\sqrt{2}}$ $V_{rms}=\frac{V_0}{\sqrt{2}}$

Where:

• $I_0$ and $V_0$ are the peak current and voltage, respectively.

Real-life Application:

Most household electrical systems operate using AC, as it is easier to transmit over long distances without significant losses.

Mnemonic:

To remember the formula for RMS values, think of "I Over Square Root Two" (I/√2) for the effective current or voltage.

2.3 Power in AC Circuits

The average power consumed in an AC circuit is given by:

$P=V_{rms}\cdot I_{rms}\cdot \cos \varphi$

Where $\varphi$ is the phase difference between the voltage and current.

NEET Problem-Solving Strategy:

Always check the phase difference in AC circuits. If the circuit is purely resistive, $\varphi =0$, and the power factor is 1.

Quick Recap

• Faraday's Law: $ϵ=-\frac{d{\Phi }_B}{dt}$
• Lenz’s Law explains the direction of induced current.
• Magnetic Flux: ${\Phi }_B=B\cdot A\cdot \cos \theta$
• AC Generator emf: $ϵ={ϵ}_0\sin (\omega t)$
• RMS values: $I_{rms}=\frac{I_0}{\sqrt{2}}$

Concept Connection

Physics to Chemistry: Electromagnetic induction is used in Magnetic Resonance Imaging (MRI), a technique heavily reliant on the principles of electromagnetism and nuclear magnetic resonance (NMR), which you will study in chemistry.

Practice Questions

1. A loop of wire is placed in a time-varying magnetic field. The magnetic flux through the loop changes from 0.2 Wb to 0.8 Wb in 2 seconds. What is the induced emf?
2. • Solution: Using Faraday’s law, $ϵ=-\frac{d{\Phi }_B}{dt}=-\frac{0.8-0.2}{2}=-0.3\text{ V}$.
2. An AC generator has 500 turns of wire, a magnetic field of 0.1 T, and a coil area of 0.05 m². If the coil rotates at 60 rad/s, calculate the peak emf generated.
3. • Solution: ${ϵ}_0=NBA\omega =500\times 0.1\times 0.05\times 60=1.5\text{ V}$.

This structure provides a comprehensive yet concise summary of the key formulas, their explanations, and relevant applications for the NEET exam, ensuring students grasp the essential concepts efficiently.