Very Very Important Questions along with their Solutions for Board Exams. Physics

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1 1 Very Very Imortant Questions along with their Solutions for Board Exams. Physics SECTION A (Each Question carries 1 Mark) 1. The lot of the variation of otential difference across a combination of three identical cells in series versus current is as shown alongside. What is the emf of each cell?. What is sky wave roagation?. Calculate the ratio of energies of hotons roduced due to transition of an electron of hydrogen atom from its, (i) second ermitted energy level to the first level, and (ii) the highest ermitted energy level to the first ermitted level. 4. Write two imortant results drawn from Rutherford s alha article scattering exeriment. 5. A carbon resistor is marked in coloured bands of red, black, orange and silver. What is the resistance and the tolerance value of the resistor? 6. Two charges of magnitudes Q and +Q are located at oints (a, 0) and (4a, 0), resectively. What is the electric flux due to these charges through a shere of radius a with its centre at the origin? 7. In the following diagrams, indicate whether the diodes are forward biased or reverse biased. 8. In the below figure, a bar magnet is quickly moved towards a conducting loo having a caacitor. Predict the olarity of the lates A and B of the caacitor. As, the magnet moves towards the coil flux linked with the coil increases, hence according to the Lenz s law it will oose the change As, the magnet moves towards the coil flux linked with the coil increases, hence according to the Lenz s law it will oose the change. SECTION B (Each Question carries Marks) 9. Give two disadvantages of transmitting AC over long distances at low voltage and high current.

2 10. A coil with an air core and an electric bulb are connected in series across a 0 V and 50 Hz AC source. The bulb glows with some brightness. How will the glow of the bulb be affected on introducing a caacitor in series, with the circuit? Justify your answer. 11. Sky waves are not used in transmitting TV signals, why? State two factors by which the range of transmission of TV signals can be increased. 1. (i) A circular coil of 0 turns and radius 8.0 cm carrying a current of 6.0 A is susended vertically in a uniform horizontal magnetic field of magnitude 1.0 T. The field lines make an angle 60 with the normal of the coil. Calculate the magnitude of the counter torque that must be alied to revent the coil from turning. (ii) Would your answer change, if the circular coil were relaced by a lanar coil of some irregular shae that encloses the same area? (All other articulars are also unaltered). Exlain the following : (i) Why do magnetic lines of force form continuous closed loos? (ii) Why are the field lines reelled (exelled) when a diamagnetic materials is laced in an external uniform magnetic field? 1. Aly Kirchhoff s laws to the loos PRSP and PRQP to write the exressions for the currents I 1, I and I in the given circuit. Aly Kirchhoff s laws to the loos ACBPA and ACBQA to write the exressions for the currents I 1, I, and I in the network. 14. Two wire loos PQRS formed by joining two semicircular wires of radii R and R 1 carry a current, i. Find the magnetic field at the centre C. 15. The electric otential, V as a function of distance (x) is shown in the figure. Construct a grah of the electric field strength, E versus distance x.

3 The grah shows the variation of charge q versus otential difference V for two caacitors, C and C. 1 The two caacitors have the same late searation but the late area of C is double than that of C 1. Which of the lines in the grah corresond to C 1 and C and why? B Variation of charge versus otential 16. Write the tye of biasing which is used in the following devices in their working. (i) Photodiode (ii) Light emitting diode 17. Give reason. (i) lighter elements are better moderators for a nuclear reactor than heavier elements. (ii) In a natural uranium reactor, heavy water is referred moderator to ordinary water. 18. Write the truth table for the circuit shown in Figure (a) and (b) consisting of N gate only. Identify the logic oeration (, AND, NOT) erformed by the two circuits. SECTION C (Each Question carries Marks) 19. A galvanometer can be converted into a voltmeter to measure u to (i) V volt by connecting a resistance R 1 in series with coil. (ii) V volt by connecting a resistance R in series with its coil. Find the resistance (R), in terms of R 1 and R required to convert it into a voltmeter that can read u to V volts. 0. Two cells of emfs, E and E and internal resistances, r and r, resectively, are connected in arallel to each other and with an external resistance R. Obtain the exression for the equivalent emf and the internal resistance of the combination.

4 4 1. A circular coil of N turns and radius, R is ket normal to a magnetic field given by B B 0 cos ω t. Deduce an exression for the emf induced in this coil. State the rule which hels to detect the direction of induced current. An inductor, L of reactance, X L is connected in series with a bulb B to an AC source as shown in the figure. Briefly exlain how does the brightness of the bulb change, when (i) number of turns of the inductor is reduced? (ii) A caacitor of reactance, XC XL is included in series in the same circuit?. (i) Why are coherent sources necessary to roduce a sustained interference attern? (ii) In Young s double slit exeriment using monochromatic light of wavelength λ, the intensity of light at a oint on the screen where ath difference is λ, is K units. Find out the intensity of light at a oint where ath difference is λ /.. An α -article and roton are accelerated from the state of rest through the same otential difference, V. Find the ratio of de-broglie wavelengths associated with them. 4. Draw the grah showing the variation of binding energy er nucleon with mass number. Give the reason for the decrease of binding energy er nucleon for nuclei with high mass numbers. 5. A convex mirror is laced in the ath of a convergent beam so that the oint of convergence of the beam lies on the rincial axis at a distance of 0 cm behind the ole. The reflected rays converge in front of the mirror at a distance of 50 cm from the ole. What is the focal length of the mirror? 6. A battery E 1 of 4 V and a variable resistance R h are connected in series with the wire AB of the otentiometer. The length of the wire of the otentiometer is 1m. When a cell of emf 1.5 V is connected between the oints A and C, no current flows through E. Length of AC 60 cm. (i) Find the otential difference between the ends A and B of the otentiometer. (ii) Would the method work, if the battery E 1 is relaced by a cell of emf of 1 V? 7. Net caacitance of three identical caacitor in series is 1µ F. What will be their net caacitance, if connected in arallel? Find the ratio fo energy stored in the two configurations, if they are both connected to the same source. 8. The intensity at the central maxima (O) in a Young s double slit exerimental is I 0. If the distance OP equals one-third of fringe width of the attern, then show that the intensity at oint P would be I 0 /4.

5 5 9. A 50 MHz sky wave takes 4.04 ms to reach a receiver via re-transmission from a satellite 600 km above Earth s surface. Assuming re-transmission time by satellite negligible, find the distance between source and receiver. If communication between the two was to be done by Line of Sight (LOS) method, what should size and lacement of receiving and transmitting antennas be? 0. (a) If a neutron and alha article having same linear momentum, then which has larger wavelength? (b) What is the shortest wavelength resent in the Paschen series of sectral lines in hydrogen atom? 1. Derive an exression for the magnetic diole moment of an electron revolving around a nucleus in terms of Planck s constant (h) and mass of electrons (m ). e. Using the data given below, state which two of the given lenses will you refer to construct a best ossible (i) telescoe (ii) microscoe. Also, indicate which of the selected lenses is to be used as an objective and as an eye lens in each case. Lens Power (P) Aerture (A) L 1 6 D 1 cm L D 8 cm L 10 D 1 cm. A beam of light consisting of two wavelengths 650 nm and 50 nm, is used to obtain interference fringes in Young s double slit exeriment. (a) Find the distance of the third bright fringe on the screen from the central maximum for the wavelength 650 nm. (b) What is the least distance from the central maximum where the bright fringes due to both wavelength coincide? The distance between the two slits is mm and the distance between the lane of the slits and the screen is 10 cm. 4. What is a Zener diode? How can a Zener diode be used as voltage regulator? Exlain using aroriate circuit diagram. 5. Outut characteristics of an n--n transistor in CE configuration is shown in the below figure. Determine : (a) DC current gain (b) Dynamic outut resistance (c) AC current gain at an oerating oint, V CE 10 V, when IB 0µ A.

6 6 6. An electron emitted by a heated cathode and accelerated through a otential difference of.0 kv, enters of region with a uniform magnetic field of 0.15 T. Determine the trajectory of the electrons if the magnetic field (i) is transverse to its initial velocity, (ii) makes an angle 0 with the initial velocity. 7. A horizontal straight wire 10 m long extending from East to West is falling with a seed of 5 m/s at right angles to the horizontal comonent of the earth s magnetic field Wbm. (i) (ii) What is the instantaneous value of the emf induced in the wire? What is the direction of the emf? (iii) Which end of the wire is at the higher electrical otential? 8. What is an astronomical telescoe? Draw the labeled ray diagram, when final image forms at least distance of distinct vision. Deduce exression for magnifying ower. 9. Sketch the grah, showing the variation of stoing otential with frequency of incident radiation for two hotosensitive metals A and B having threshold frequencies v 0 and v 0 resectively (v 0 > v 0 ). (i) (ii) Which of the two metals, A or B has higher work function? What information do you get from the sloe of the grahs? (iii) What does the value of the intercet of grah on the otential axis reresent? 40. A caacitor made of two circular lates each of radius, r 1 cm and charging current is constan, t I 0.15 A. (i) (ii) Calculate the rate of change of electric field between the lates. Find the dislacement current across the lates. (iii) Is Kirchhoff s first rule valid at each late of caacitor? Exlain. 41. A 00 V variable frequency AC source is connected to a series combination of L 5H, C 80 µ F and R 40 Ω. Calculate (i) angular frequency of source to get the maximum current in the circuit. (ii) current amlitude at resonance. (iv) ower dissiation in the circuit. 4. In the accomanying diagram, the direct image is formed by the lens (f 10 cm) of an object laced at O and that formed after reflection from the sherical mirror is formed at the same oint O. What is the radius of curvature of the mirror?

7 7 4. A rectangular loo shaed wire KLMN is moved with a uniform velocity, v at right angle to a uniform magnetic field, B as shown in the figure. (i) (ii) What is the magnitude of current induced in the loo? Will there be any work done by the loo? Give reason for your answer. SECTION D (Each Question carries 4 Marks) 44. Merrie Curie and her teacher turned husband Pierre Curie worked hard to extract radium chloride (RaCl ) from uranium ore. They succeed in 190 after a long struggle. About 0.19 g of RaCl was extracted and its radioactivity was studied. They were awarded by the nobel rize, which they shared it with Henri Becquerel. (i) What are the values shown by Merrie Curie and her husband? (ii) What do you understand by radioactivity? How the half-life eriod is related to the disintegration constant? (iii) The sequence of stewise decays of a radioactive nucleus is α β α 1 D D D D If the nucleon number and atomic number of D are 176 and 71, resectively, then what are the corresonding values of and D? Justify your answer in each case. SECTION E (Each Question carries 5 Marks) 45. An inductor L, a caacitor C and a resistor R are connected in series in an AC circuit. Deduce with the hel of suitable hasor diagram, a mathematical exression for imedance of this circuit. What is meant by resonance of this circuit? Prove that this circuit exhibits resonance at a frequency given by 1. π LC (i) A series L-C-R circuit is connected to an AC source of voltage V and angular frequency ω when only the caacitor is removed, the current lags behind the voltage by a hase angle ' φ ' and when only the inductor is removed, the current leads the voltage by the same hase angle. Find the current flowing and the average ower dissiated in the L-C-R circuit.

8 8 (ii) An alternating voltage given by V 140 sin 14 t is connected across a ure resistor of 50 π. Find (a) The frequency of the source (b) the rms current through the resistor. 46. Show that the refractive index of the material of a rism is given by (A + δm ) sin µ A sin Where, the symbols have their usual meanings. Define the term resolving ower of an astronomical telescoe. How does it get affected on (i) Increasing the aerture of the objective lens? (ii) Increasing the wavelength of light used? (iii) Increasing the focal length of the objective lens? 47. Find an exression for the torque acting on and electric diole laced in uniform electric field. A 7 7 system of two charges qa.5 10 C and qb.5 10 C located at oints A (0, 0, 15) cm and B (0, 0, +15) cm, resectively. Find the electric diole moment of the system and the magnitude of the 4 1 torque acting on it, when it is laced in a uniform electric field 5 10 NC, making an angle 0. A caacitor of caacitance C is charged fully by connecting it to a battery of emf E. It is then disconnected from the battery. If the searation between the lates of the caacitor is now doubled, what will haen to (i) Charge stored by the caacitor? (iii) field strength between the lates? (iv) caacitance of the caacitor? (ii) Potential difference across it? (iv) energy stored by the caacitor? 48. Exlain the rincile, working and theory of a transformer by using its diagram. Also, exlain the use of transformer in long distance transmission of electric ower with the hel of schematic diagram. (a) Mention the reasons for energy losses in an actual transformer. (b) The ower transmission lines needs inut ower at 00 V to a ste down transformer with its rimary windings having 4000 turns. What should be the number of turns in the secondary windings in order to get outut ower at 0 V. 49. (i) What do you mean by current sensitivity of a moving coil galvanometer. On what factor does it deend? (ii) State two reason why a galvanometer cannot be used as such to measure high order current in a given circuit? (iii) The current sensitivity of a moving coil galvanometer is 5 division/ma and voltage sensitivity is 0 division/volt. Find the resistance of the galvanometer. (i) Write any three characteristics, a ferromagnetic substance should ossess, if it is to be used to make a ermanent magnet. Give one examle of such a material. (ii) The suscetibility of a magnetic material is Identify the magnetic tye of the material.

9 9 (iii) A Rowland ring of mean radius 15 cm has 500 turns of wire wound on a ferromagnetic core of relative ermeability 800. What is the magnetic field (B) in the core for a magnetizing current of 1. A? SOLUTIONS 1.In oen circuit, when no current is being drawn from the cells, the terminal otential difference is equal to emf of cells. Emf of the series combination of three cells 6V 6V Emf of each cell, ε V. A radiowave of frequency range MHz to 0 MHz can be directed towards the sky and reflected by the ionoshere towards desired location of the Earth, called as sky wave roagation.. Energy of hoton 1 1 hv n 1 n 1 1 hv 1 1 : 4 hv ( ) ( ) 4. (i) The most of the mass and the entire ositive charge of an atom is concentrated in a very small volume of the atom, called nucleus. (ii) The nuclear radius is about 1/10000 of the atomic radius. 5. According to colour code of carbon resistor, a carbon resistance of bands of red and black having figures and 0. The third band of orange having multilier 10. The value of resistance is given by R 0 10 Ω But the fourth band having silver colour which reresents a tolerance of ±10%. Hence, the value of carbon resistor, R 0 10 Ω ± 10% q 6. Gauss s theorem states that the total electric flux linked with closed surface, S is φ E φ E.dS, ε where, q is the total charge enclosed by the closed Gaussian (imaginary) surface. 0 Q The shere enclose charge Q + Q Q. Therefore, φ. ε 7. (i) Forward biased, because -side is at higher otential (+7 V) then n-side (+5 V). (ii) Forward biased, because -side is at higher otential ( 5 V) than n-side ( 1 V). 0

10 10 8. Here, the North ole is aroaching the magnet, so the induced current in the face of loo viewed from left side will flow in such a way that it will behave like North ole, so, South ole develoed in loo when viewed from right hand side of the loo. The flow of induced current is clockwise. Hence, A acquires ositive olarity and B acquires negative olarity. 9. Following are the disadvantages of transmitting electrical ower at low voltage. (i) Large lengths of transmission cables have sufficient resistance. Hence, a large amount of energy (I Rt) will be lost as heat during transmission. (ii) Large voltage dro (IR) occurs along the line wire. Hence, the voltage at the receiving station will be much smaller than that at the generating station. 10. A coil with an air core has very small inductance and therefore, inductive reactance, XL 0. When a caacitor is introduced in series, the imedance becomes On increasing imedance of the circuit, the current in the circuit reduces of the bulb decrease. Z R + X C, which is greater than R. V Q i and the brightness Z The shere enclose charge Q + Q Q Therefore, Q φ. ε TV signals have a frequency of 100 to 0 MHz which cannot be reflected by the ionoshere. So, transmission of TV signals via sky wave is not ossible. Range of TV transmission can be increased by using (i) Tall antenna (ii) Geostationary satellites 1. Here, N 0, R 8.0 cm 8 10 m, I 6.0 A, θ 60 and B 1.0 T (i) The magnitude of the counter torque magnitude of the deflecting torque NAIB sinθ N.( πr ) IB sinθ 0.14 (8 10 ) sin Nm (ii) The answer would not change as area enclosed by the coil as well as all other articular remain unaltered and the formula, τ NAIB sin θ is true for lanar coil for any shae. 1. Aly Kirchhoff s 1 st law at oint P of the circuit I I + I 1 Alying Kirchhoff s nd law to loo PRSP 0I 00I + 5 0, 40I + 4I 1 Alying Kirchhoff s nd law to loo PRQP 0I 60I , 15I1 + 5I Let ˆn be the unit vector erendicular to the lane of aer outwards. Magnetic field at C due to current through the entire structure PQRS is

11 11 µ 0 πi µ 0 πi B BSR + BRQ + BQP + BPS 0 + nˆ ( n) ˆ 4π R 4π R 1 (i) µ 0 I 1 1 B nˆ 4 R1 R µ 0 I 1 1 B 4 R1 R uwards dv 15. Electric field intensity E and electric otential V are related as E, where x is distance. So dx negative sloe of V versus x grah will give the value of electric field. Grah of the electric field strength, E versus distance x is given below. Electric field strength versus distance Q Electric field intensity and electric otential are related as Here, when 0 > x > 1, sloe is ositive. dv E Negative slo of V x grah. dx Then, dv 0 dx > Electric field intensity is constant E; For 1 < x < sloe 0 E 0 For Q dv < x <, < 0 Electric field, E > 0 i.e. E + ve + E dx q C [C is caacitance, q is charge on caacitor and V is otential] V So, sloe of q versus V grah will give caacitance, also we know that, ε C d [ε 0 is ermittivity of free sace, A is area of late of caacitor, d is distance between lates of caacitor] The sloe of grah Also, Q d is a constant. C A q C (caacitance of caacitor) V sloe of grah A (area of late) 0 A

12 1 Higher the area of lates of caacitor Higher the sloe of grah. So, grah A reresents C and grah B reresents C (i) Photodiode is used in reverse biasing. (ii) Light Emitting Diode (LED) is used in forward biasing. 17. (i) A moderator slows down fast neutrons released in a nuclear reactor. The basic rincile of mechanics is that the energy transfer in a collision is the maximum when the colliding articles have equal masses. As, lighter elements have mass close to that of neutrons, lighter elements are better moderators than heavier elements. 1 (ii) Ordinary water has hydrogen nuclei ( 1 ) H which have greater absortion cature for neutrons; so ordinary water will absorb neutrons rather than slowing them. On the other hand, the heavy hydrogen nuclei ( 1 ) H have negligible absortion cature for neutrons, so they share energy with neutrons and neutrons are slowed down. 18. The logic oeration of fig. (a) is Y A + A A. This is logic oeration of NOT gate. The truth table of this circuit is A Y A The logic oeration of Fig. (b) is Y A + B A.B A.B The truth table of this circuit is A B Y Formula for conversion of galvanometer into voltmeter is i g V R + G Where, G is galvanometer resistance. In case (i) In case (ii), i i g g V R + G 1 V/ R + G From Eqs. (i) and (ii), we get 1 (i).(ii) V V R1 + G R + G R + G (R + G) G R1 R (iii)

13 1 For conversion of galvanometer into a voltmeter of range V, we have i g V R + G. (iv) From Eqs. (i) and (iv), we get R + G R1 + G R R1 + G V V R + G R + G Putting the value of G from Eq. (iii), we get R R 1 + (R1 R ) R R1 R 1 0. Suose, the cell combination is connected with resistance R (say) as shown in figure below. Alying Kirchhoff s first law. I I1 + I..(i) Alying KVL rule, E IR I 1 (r) 0 IR E I1 r.(ii) Again alying KVL rule, E IR Ir 0 Or IR E Ir (iii) Or IR E (I I 1)r [ from Eq. (i)] Or IR E Ir + I1r Or IR + Ir E + I1r Or I (R + r) E + I1 r (iv) Multilying Eq. (iv) by and adding with Eq. (ii), we get I (R + r) + IR (E I1 r) + (E + I1 r) Or, IR + Ir 4E Or, I (R + r) 4E Or 4E I r R +

14 14 4E Or, I (v) r R + If equivalent emf and internal resistance of a battery be Eeq and r eq, then current E0 I R + r 0 Comaring Eqs. (v) and (vi) we get 4E Equivalent emf, Eeq volt r Internal resistance, r eq Ω 1. Induced emf in the coil dφ d e N N (BA cos 0 ) [ Q φ BA cos θ] dt dt db NA [ Q cos0 1] dt (vi) d NπR (B0 cos ω t) dt NπR ωb sin ω t 0 [ Q A πr ] d [ Q cos ω t ω sin ωt] dt The direction of induced current is given by Lenz s law which states, the direction of induced current is always in such a way that it ooses the cause due to which it is roduced. (i) When the number of turns of the inductor is reduced, its inductance, X L decreases. A decrease in inductance causes the current in the circuit to increase and hence, the brightness of the bulb increases. (ii) When the caacitor is connected in series in the circuit, then its imedance is given by Here, XL XC XL XC Z R L C Z R + (X X ) Thus, the imedance is minimum and is equal to the resistance and hence, the brightness of the bulb is maximum.. (i) Coherent sources roduces light of constant hase difference and hence ermanent fringe attern roduces due to interference of light. (ii) Intensity of light at a oint on the screen is given by IR I1 + I + I1I cos φ

15 15 (a) For the ath difference of λ, hase difference is π. As, source are coherent and taken out L of the same source in Young s double slit exeriment, I1 I I IR I + I cos π IR 4I 4I v unit.(i) λ π (b) Path difference of corresonds to hase difference π IR I + I cos I I I.(ii) From Eqs. (i) and (ii) we get I R K units 4. de-broglie wavelength, λ h h, me where is momentum and E k is kinetic energy of a article. k For charged article accelerated through a otential difference V, kinetic energy of article Ek qv de-broglie wavelength, λ h mqv For α article, m 4m, q e h h λ α 4m ev 4 m ev For roton, m m, q e, λ h m ev Ratio of de-broglie wavelengths, λ α λ 1 8 λ : λ 1: α 4.

16 16 Reason : Due to increase in coulomb reulsive force between rotons, binding energy er nucleon deceases for nuclei with higher mass numbers. 5. We have distance of object from mirror, u (+) 0 cm Distance of image from mirror, v ( ) 50cm From mirror formula v u f 50 0 f E l 6. (i) We know that, E' l' Here, E 1.5 V, l 60 cm, l' 100 cm or focal length of the mirror, f + 75 cm. l' Potential difference, E' E 1.5V V.5 V l The otential difference between the ends A and B of the otentiometer is.5 V. (ii) No, the method will not work because if the battery E 1 is relaced by a cell of emf of 1 V in that case, then the balance oint or deflection oint will not be obtained. 7. If n identical caacitors, each of caacitance, C are connected in series combination gives equivalent caacitance, C s C n And when connected in arallel, then equivalent caacitance. C nc C nc n C C / n s Or C n C s Also, for same voltage, energy stored in caacitor is given by According to roblem, C nc s 1 U CV [for V constant] 1µ F µ F For each caacitor, in arallel combination, C nc 9µ F or C 9µ F For same voltage,

17 17 U U C C/n s s C U C nc n () s 9 U 1 or U s : U 1: 9 U 9 8. Intensity can be found out, if we know the hase difference. Phase difference can be calculated with the hel of ath difference. So, first of all ath difference will be calculated. Given, OP Y n The distance OP equals one-third of fringe width of the attern, i.e. Path difference Y Phase difference, n β 1 Dλ Dλ d d dyn λ SP S1P D π φ ath difference λ π λ π λ dyn λ D If intensity at central fringe is I 0, then intensity at a oint P, where hase difference is φ, is given by 0 I I cos φ π I I0 cos π I0 cos 1 I0 I0 4 Hence, the intensity at the oint P would be I Let the receiver be at oint A and source be at B. Velocity of waves 8 10 m/s Time to reach a receiver 4.04 ms s Let the height of satellite is hs Radius of Earth 6400 km Size of transmitting antenna h T We know that, 600 km

18 Distance travelled by wave velocity of waves Time x Or x km Using Pythagoras theorem, s d x h (606) (600) 76 or d km So, the distance between source and receive d km The maximum distance covered on ground from the transmitter by emitted EM waves, d Rh T Or d h R or size of antenna, 0. (a) Since, T h λ 76 ht km 565m 6400 Where, λ wavelength h Planck s constant and linear momentum As both articles have same linear momentum, therefore both articles have same wavelength (b) The wavelength in Paschen series is given by R λ n Where, R Rydberg constant and n 4, 5, 6,.. For shortest wavelength n R R λ () λ () or () 9 λ R Shortest wavelength 7 λ m or λ 804 Å 1. Let an electron revolves around the nucleus with uniform seed v. This motion is equivalent to electric current loo of magnetic diole moment.

19 19 µ IA I( π r ) π Ir.(i) Let t be the time eriod of electron. Therefore, πr T.(ii) V Where, r is the radius of circular ath of electron. Now, the equivalent current e e I T πr v ev I πr Magnetic diole moment ev µ π Ir π r π [from Eq. (ii)] (iii) evr µ (iv) Now, the angular momentum of electron L m vr (v) e [from Eq. (iii)] evr µ e or L (m vr) m e e e µ L me By Bohr s second ostulate of quantization, (vi) Angular momentum, nh L where, n 1,,. And h Plank s constant π From Eq. (vi) e nh µ m π e eh Magnetic diole moment µ n 4 π m e This is the required exression.