Assignment – 5

ELECTROMAGNETIC INDUCTION, ALTERNATING CURRENT AND ELECTROMAGNETIC WAVES.

GUIDE LINE FOR PREPARING CBSE (PHYSICS) EXAMINATION THROUGH

PREVIOUS YEARS QUESTIONS OF CBSE MARKED WITH STARS ( )

THESE QUESTIONS ALSO APPEARED OFTEN IN QUATERLY, HALFYEARLY AND PRE-BOARD EXAINATION S OF DIFFERENT PUBLIC SCHOOLS OF DELHI. (Generally five-, three-, two- and one- marks questions are generated from the theory

and derivation part of the questions mentioned below including final formula)

1. (a)Write the Faradey’s law of electromagnetic induction with mathematical explanation.(b) Write Lenz’s law. How you can verify this law experimentally. Show that the law is in accordance with the law of conservation of energy.

2. Define Self and Mutual inductance and give its S.I unit. . Find an expression for self inductance of a solenoid. What happens to the self inductance of a solenoid if: (i) number of turns in the solenoid is doubled and (ii) a soft iron core is introduced along the axis of the solenoid.

3. Derive an expression for the mutual inductance of two long coaxial solenoids of same length wound one over the other. State four factors on which mutual inductance depend.

4. Two circular coils, one of radius R1 and N1 turns and other of radius R2 and N2 turns, are place co-axially with their centers coinciding. For R1 >> R2 obtain an expression for the mutual inductance between these coils.

5. Derive an expression for (i) induced emf and (ii) induced current when a conductor of length l is move with a uniform velocity v, normal to a uniform magnetic filed B. Assume the resistance of conductor to be R. A conducting rod of length l, with one end pivoted, is rotated with a uniform angular speed in a vertical plane, normal to a uniform magnetic field B .Deduce an expression for the emf induced in this rod.

6. Show that the dimension of RC and L/R are the dimension of time. (i) Derive expression for average current or voltage. Why the limits are taken from 0 to T/2. (ii)Derive expression for root mean square current or voltage. Why in this case the limits are taken from 0 to T.

7. A pure resistor, inductor and a capacitor is connected one by one across an a.c. source. Find the change in phase between current and voltage and draw the

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corresponding phasor diagram. Also draw the phasor diagram when a pure resistor, inductor and a capacitor is connected in series across an a.c. source. What is the role of pure inductor when it is connected with d.c circuit? What is the role of a capacitor when it is connected in a.c circuit?

8. Show that the average power associated with (i) inductor and (ii) capacitor is zero Derive also expression for average power associated with series L-C-R circuit.What is the power dissipated in an ac circuit in which voltage and current are given by V = 230 sin [ t + /2 ] and I = 10 sint .The power factor of an ac circuit is 0.5. What will be the phase difference between voltage and current in this circuit? ..

9. Derive an expression for the average Power in LCR-circuit.*10. Derive an expression for impedance for series LCR -circuit. Draw the graphs

showing the variations of inductive reactance and capacitive reactance with frequency of applied a.c source. Find out an expression for resonance frequency in series LCR- circuit. If the resistance ( R ) is doubled what will happen to resonant frequency. At resonance what would be the value of (i) Impedance and (ii) Power factor. Can the voltage drop across the inductor or capacitor in a series LCR circuit be greater than the applied voltage of the ac source? Justify your answer.

11. An inductor, a bulb are in series with a a.c source. What will happen to the intensity of the bulb if (i) the frequency of the source is increased and (ii) one iron rod is introduced inside the incuctor.*

12. A capacitor, a bulb are in series with a a.c source. What will happen to the intensity of the bulb if (i) the frequency of the source is increased and (ii) dielectric is introduced inside the capacitor.*

13. An inductor, capacitor, resistor and a bulb are in series with a a.c source. What will happen to the intensity of the bulb if the frequency of the source is increased from low value to high value above the resonant frequency?*

14. Define and derive an expression for quality factor Q. How Q changes with R and L of the L-C-R-circuit Or name the two factors on which Q depends.[CBSE 2009]

Obtain the resonant frequency r of series LCR circuit with L=2.0 H, C = 32 F and R = 10 . Hence find the quality factor Q of the circuit.****

An inductor 200 mH , capacitor 500 F, resistor 10 are connected in series with a 100 V, variable frequency a.c source. Calculate: (i) frequency at which the power factor of the circuit is unit, (ii) current amplitude at this frequency and (iii) Q- factor.

15. Name two material used for making transformer cores. Explain why these materials are used. What is the principle of transformer? Explain with a labeled diagram. Why electrical power is generally transmitted over long distance at high a.c

voltage? Explain the use of transformer in such transmission? What are the different types of energy loses in a transformer, explain?

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Can a transformer work if primary is connected to a d.c source. Explain? 16. With the help of a labeled diagram explain the working of an a.c generator

and show graphically the variation of induced e.m.f with time, given that at time t = 0, the plane of coil is normal to the direction of the magnetic field. A coil of number of turns N and are A is rotated at a constant angular speed in a uniform magnetic field B, and connected to a resistor R. Deduce expression for: (i) Maximum emf induced in the coil and (ii) Power dissipation in the coil.

17. Draw a labeled diagram of Hertz’s experimental set-up to produce electromagnetic waves. Explain the generation and detection of electromagnetic waves using this set-up.

18. (a)Draw a graph showing the propagation of electromagnetic wave with electric vector and magnetic vector. In which direction energy propagates. Is it transverse or longitudinal wave? Prove that the velocity of electromagnetic wave is equal to the velocity of light.

19. Arrange the electromagnetic waves in increasing order of frequency. Name the wave having highest and lowest frequencies. Write the uses of Microwave, Infrared, Ultraviolet and X-Ray radiation. Name the electromagnetic wave which is having highest penetrating power. Which part of the frequency spectrum is harmful for human skin, name it.

20. The magnetic field of a plane electromagnetic wave is given by: By = 8 x 10-7 sin {300 x + 2 x 1011 t} T

(i)What is the wavelength and frequency of the wave and (ii)Write an expression for the electric field. 21. Give the difference between displacement current and conduction current. Draw

wave-form of EM-waves progressing along Y-direction. ****22. A plane electromagnetic wave of frequency 25 MHz travels in free space along the

X-direction. At a particular point in space and time, E = 6.3 j V/m. What is B at this point? [Ans: 2.1 10-8 T]. (NCRT SLVD EXAM)

23. The electric field of plane electromagnetic wave in vacuum is represented by:Ex = 0 ; Ey = 0.5 cos{ 2 ∏ x 108 ( t – x/c)} ; Ez = 0(i)What is the direction of propagation of electromagnetic waves?(ii)Determine the wavelength of the wave(iii) Compute the component of associated magnetic field.[Ans: Along X-axis; = 3 m; Bx = 0;By = 0; By =( 0.5/ 3 x 108 ) cos{ 2 ∏ x 108 ( t – x/c)} (CBSE;NVT P S;DPS MATH RD)

24. A plane monochromatic light wave line is in the visible region. It is represented by the sinusoidal variation with time by the following components of electric field: Ex = 0 ; Ey = 4 sin { 2 ∏/ ( t – x)} ; Ez = 0, where is 5 x 1014 Hz, and is the

wavelength of light: (i)What is the direction of propagation of the wave? (ii) what is its amplitude and (iii)compute the components of magnetic field. (BAL BH.P S; D P S NOIDA)

25. The magnetic field of a plane electromagnetic wave is given by: By = 2 x 10-7 sin{ 0.5 x 103 x + 1.5 x 1011 t } T

(i)What is the wavelength and frequency of the wave and

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(ii)Write an expression for the electric field. [ Ans:= 1.26 cm. =23.9 GHz, Ez = 60 sin{ 0.5 x 103 x + 1.5 x 1011 t } v/m] (NCRT SLVD EXAM)

26. Light with an energy flux of 18 W/cm2 falls on a non reflecting surface at normal incidence. If the surface has an area of 20 cm2. Find the average force exerted pm the surface during a 30 minute time span. (NCRT SLVD EXAM)

27. Calculate the electric and magnetic fields produced by the radiation coming from a 100W bulb at a distance of 3 m. Assuming that the efficiency of the bulb is 2.5 % and it is a point source.(NCRT SLVD EXAM)

28. Suppose that the electric field part of an electromagnetic wave in vacuum is given by: E = (3.1 N/C) cos {1.8 rad/m y + 5.4 x 106 rad/s t}i

(i) What is the direction of propagation?(ii) What is the wavelength?(iii)What is the frequency?(iv)What is amplitude of the magnetic field part of the wave?(v) Write an expression for the magnetic field part of the wave. [Ans: (i) -j (ii)3.5 m (iii) 86 MHz (iv) 100nT (v) ( 100 nT) cos {1.8 rad/m y + 5.4 x 106 rad/s t}k (NCRT SLVD EXAM)

29. A radio transmitter operates at a frequency of 880 kHz and a power of 10 Kw. Find the number of photons per second emitted. **

30. For earth to satellite communication which frequency you will prefer out of the two: (i) Radio frequency wave (ii) microwave frequency. Why explain. **

31. Identify the constituent radiation electromagnetic spectrum which (i) is used for studying crystal structure, (ii) is absorbed by the ozone layer in the atmosphere and (iii) produces intense heating effect. Mention one more application for each of these radiations. ***

32. Name the electromagnetic wave which is used for heating oven. Which frequency is used and why? (New important question)

33. Why microwave is used in RADAR. **34. What is the name given to that part of electromagnetic spectrum which is used for

taking photographs of earth under foggy conditions from great heights?***

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