# Electromagnetic Induction and Alternating currents   Share

## What is Electromagnetic Induction and Alternating currents

We have studied about electric fields created by fixed charge distributions and magnetic fields produced by constant currents, but electromagnetic phenomena are not restricted to these stationary situations. Electromagnetism has many interesting applications which are, in fact, time-dependent. In this chapter, we will remove the time-independent assumption that we have been making and allow the fields to vary with time and we will see a wonderful symmetry in the behavior exhibited by time-varying electric and magnetic fields. Mathematically, this symmetry is expressed by an additional term in Ampère’s law and by another key equation of electromagnetism called Faraday’s law. The phenomenon in which electric current is generated due to varying magnetic fields is called electromagnetic induction.

We can easily understand the symmetry between electricity and magnetism by looking at nature. Nature displays symmetry in Butterfly’s wings, similarly, laws of physics display symmetry at the most basic level and also it is known that a current creates a magnetic field. If nature is symmetric here, then perhaps current can be created by a magnetic field. Magnetic force cause a voltage, i.e., the Hall effect and that voltage could drive a current. Today, currents which are being induced by magnetic fields are essential to a technological society. The generator—found in automobiles, on bicycles, in nuclear power plants, and so on—uses magnetism to generate current. Other devices that use magnetism to induce currents include transformers of every size, certain microphones, airport security gates. The behavior of AC circuits depends on the effects of magnetic fields on currents. Another application of induction is the magnetic stripe on the back of your personal credit card as used at the grocery store or the ATM machine. This works on the same principle as that of the audio or videotape, in which a playback head reads personal information from your card.

## Notes for Electromagnetic Induction and Alternating currents

Now we will discuss each of the important topics along with an Overview of the chapter followed by important formulas of the chapter which will help you in solving numerically related to Electromagnetic Induction and Alternating currents.

## Topics for Electromagnetic Induction and Alternating currents

• Magnetic flux

• Faraday's law

• Induced emf and current

• Lenz's Law

• Eddy current

• Self and mutual inductance

• Alternating currents, peak and rms values of the alternating current/ voltage

• Reactance and impedance

• LCR series circuit

• Resonance

• Quality factor

• Power in AC circuits

• Wattless Current

• AC generator and transformer

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## Overview of  Electromagnetic Induction and Alternating currents

The phenomenon of electromagnetic induction is not only for theory or academic purposes but also useful in practical applications. Try to imagine a world where there is no electricity, no trains, no telephones, and no personal computers, then how will everyone be able to communicate or spend their time. The discovery and understanding of electromagnetic induction are based on a series of experiments carried out by Faraday and Henry.

It was observed that when the North-pole of a bar magnet is pushed towards the coil connected to a galvanometer, the pointer in the galvanometer deflects, indicating the presence of electric current in the coil. The deflection lasts as long as the bar magnet is in motion and does not show any deflection when the magnet is held stationary. When the magnet is moved away from the coil, the galvanometer shows deflection in the opposite direction, which shows a reversal of the current’s direction. When the South-pole of the bar magnet is pushed towards or away from the coil, the deflections in the galvanometer are opposite to that observed in the North-pole for similar movements.

In this chapter, we will study magnetic flux and how it is related to current and induced emf using Lenz’s law. We will discuss how Lenz's law is consistent with the law of conservation of energy. We will study the motion of the straight conductor in a uniform and time-independent magnetic field. There is an interesting relationship between the charge flow through the circuit and the change in the magnetic flux that you will get to know. You will also learn the basic principles of AC generator. In this chapter, we will use Kirchhoff’s laws to analyze four simple circuits in which ac flows. We will discuss the use of the resistor, capacitor, and inductor in circuits with batteries. These components are also part of ac circuits. However, because the alternating current is required, the constant source of emf supplied by a battery is replaced by an ac voltage source, which produces an oscillating emf.

## Formulas for Electromagnetic Induction and Alternating currents

1. Net flux through the surface: $\phi=\oint \vec{B}.d\vec{A}=BAcos\theta$

2. Rate of change of magnetic flux: $\epsilon =-\frac{d\phi}{dt}$

3. Rate of change of magnetic flux for N turns: $\epsilon =-N \frac{d\phi}{dt}$; $\phi=BAcos\theta$

4. Rate of change of magnetic flux due to change in area: $\phi=-NBcos\theta\frac{dA}{dt}$

5. Rate of change of magnetic flux due to change in magnetic field:$\phi=-Nacos\theta\frac{dB}{dt}$

6. Induced current: $I=\frac{\varepsilon }{R}=-\frac{N}{R}\frac{d\phi}{dt}$

7. Induced charge: $dq=idt=-\frac{N}{R}\frac{d\phi}{dt}dt=-\frac{N}{R}d\phi$

8. Induced power: $P=\frac{\varepsilon ^2}{R}=\frac{N^2}{R}(\frac{d\phi}{dt})^2$

9. Induced electric field: $E=\frac{a^2}{2r}\frac{dB}{dt}$

10. Motional EMF: $\varepsilon =Bl\nu$

11. Magnetic force: $F=\frac{B^2 \nu l^2 }{R}$

12. Power dissipated in moving the conductor: $F=\frac{B^2 \nu^2 l^2 }{R}$

13. Motional E.m.f due to rotational motion: $\varepsilon =\frac{1}{2}Bl^2\omega =Bl^2\pi\nu$

14. Coefficient of self induction: $L=\frac{N\phi}{I}$

15. Energy stored in the inductor: $U=\frac{1}{2}LI^2$$u=\frac{U}{V}=\frac{B^2}{2\mu_0}$

16. Energy Density( u):

17. Inductive susceptance : $S_L=\frac{1}{2\pi\nu L}$$S_L=\frac{1}{X_L}=\frac{1}{2\pi\nu L}$$X_L=w_L$

18. Capacitive susceptance : ;$S_C=\frac{1}{X_C}=2\pi\nu C$ ; $X_C=\frac{1}{w_C}$

19. Power: $P=VIcos\phi$

20. Average power : $P_{av}=V_{rms} i_{rms}cos\phi \Rightarrow P_{av}= \frac{v_0}{\sqrt{2}} \frac{i'_0}{\sqrt{2}}cos\phi \Rightarrow P_{av}=i'^2_{rms}R= \frac{V'^2_{rms}R}{Z^2}$

21. Power factor: $cos\phi=\frac{R}{Z}$

## How to prepare for Electromagnetic Induction and Alternating currents

• To prepare for this chapter, you should have good command over the concepts of Electromagnetic Induction and Alternating currents and you should also know how to apply them well at the time of the entrance exam or while solving questions.
• Please try to understand each concept from this chapter, with the help of theory, questions with solutions and video lectures on each important concept. For each concept practice enough problems to have a thorough understanding of the concept. Solve all the questions at home with proper concentration and try to do all calculations by yourself without seeing the solution first.
• Understand the derivation of each formula very clearly because if you don't remember the formulas, you can easily derive them but try to remember all the formulas from this chapter because in certain questions you will get the answer by directly applying these formulas. Understand all the laws from this chapter along with their applications. With proper study, you can solve questions from this chapter with ease.

## Tips for Electromagnetic Induction and Alternating currents

1. Make a plan to prepare for this chapter and Stick to a Timetable.

2. Study the concept first and then start solving the question. Don't go through question directly without knowing the concept.

3. Solve previous year question from this chapter.

4. Practice as many questions as possible.

“Successful and unsuccessful people do not vary greatly in their abilities. They vary in their desires to reach their potential.” - John Maxwell

## Books for Electromagnetic Induction and Alternating currents

For Electromagnetic Induction and Alternating Currents, chapter concepts in NCERT are enough but you will have to practice lots of questions including previous year questions and you can follow other standard books available for competitive exam preparation like Concepts of Physics (H. C. Verma) and Understanding Physics by D. C. Pandey (Arihant Publications).

## Physics Chapter wise Notes For Engineering and Medical Exams

 Chapters No. Chapters Name Chapter 1 Physics and Measurement Chapter 2 Kinematics Chapter 3 Laws of motion Chapter 4 Work Energy and Power Chapter 5 Rotational Motion Chapter 6 Gravitation Chapter 7 Properties of Solids and Liquids Chapter 8 Kinetic theory of Gases Chapter 9 Thermodynamics Chapter 10 Oscillations and Waves Chapter 11 Electrostatics Chapter 12 Current Electricity Chapter 13 Magnetic Effects of Current and Magnetism Chapter 15 Electromagnetic Waves Chapter 16 Optics Chapter 17 Dual Nature of Matter and Radiation Chapter 18 Atoms And Nuclei Chapter 19 Electronic devices Chapter 20 Communication Systems Chapter 21 Experimental skills

### Topics from Electromagnetic Induction and Alternating currents

• Electromagnetic Induction: Faraday's law, Induced emf and current ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (42 concepts)
• Lenz's law, Eddy currents ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (36 concepts)
• Self and mutual inductance ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (34 concepts)
• Alternating currents, peak and rms value of alternating current/voltage ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (64 concepts)
• Quality factor, power in AC circuits, wattless current ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (138 concepts)
• Reactance and Impedance ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (16 concepts)
• LCR series circuit, resonance ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (22 concepts)
• AC generator and transformer ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (52 concepts)
• Introduction to electromagnetic induction ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (9 concepts)
• AC circuits ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (36 concepts)
• Motional Electromotive force ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (15 concepts)
• Induced electric field ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (9 concepts)
• Inductance ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (18 concepts)
• AC generator ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (3 concepts)
• Transformers ( JEE Main, VITEEE, MET, KVPY SA, KVPY SB/SX, COMEDK UGET, KEAM ) (3 concepts)

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