Pyq of cbse of a subject class 12, Study Guides, Projects, Research of Mathematics

Download Pyq of cbse of a subject class 12 and more Study Guides, Projects, Research Mathematics in PDF only on Docsity! * revious Yeal Examination Questions 1 Mark Questions _ I-A charge is placed at the centre of a hollow conducting sphere of inner radius r and outer radius 2r. The ratio of the surface charge density of the inner surface to that of the outer surface will a. . Dethi 2020 Torque acting on an electric dipole placed in an uniform electric field is maximum when the angle between the electric field and the dipole moment is ......... . All india 2020 raw the pattern of electric field lines, when a point charge — @ is kept near an uncharged conducting plate. Delhi 2019 ABraw a pattern of electric field lines due to two positive charges placed a distance d apart. allindia 2019 5, the pattern of electric field lines —- an electric dipole. all india 2019 6. Why do the electrostatic field lines not form closed loop? All india 2014, Delhi 2012 Two identical balls having same positive charge g coulomb are suspended by two insulating strings of equal length. What would be the effect on the force when a plastic sheet is inserted between the two? All india 2014 “4 do the electric field lines never cross i other? All india 2014 . Why must electrostatic field at the 8 of a charged conductor be dicular to every point on it? Foreign 2014, Delhi 2012 Two point charges q, and q, are placed at a distance d apart as shown in the figure. The electric field intensity is zero at the point P on the line joining them as 11, Define dipole moment of an Is it a scalar quantity or a vector ieee Foreign 2012; All india 2071 « Draw a plot showing the variation of electric field £ with distance r due to a point charge q. Dethi 2012 a 13-4 proton is placed in a uniform electric directed along the positive X-axis. In direction, will it tend to move? Delhi zone 4in which orientation, a dipole placed in uniform electric field is in (i) stable equilibrium (ii) unstable equilibrium? one i 3 Two point charges having equal charges — separated by 1m distance experience a force of 8 N. What will be the force experienced by them, if they are held in water at the same distance? (Given, K ater = 80). Allindia 20106 metallic sphere is placed in a uniform electric field as shown in the figure. Whiel path is followed by electric field lines and why? Foreign 2010 16, / fo 47. Point out whether the following statei is right or wrong. a b ic d The mutual forces between two cha not get affected by the presence of charges. All India 2010 (Z 2 Marks Questions 18. Derive the expression for the torque act on an electric dipole when it is held im! uniform electric field. Identify the orientation of the dipole in the i field in which it attains a stable equilibrium, Dethi 2020  10. ‘expression for the electric field due (.28-Two concentric of dipole moment p at a point on aholls of radii Rand Pr] jar bisector. Dethi 2019 ee and Q, re’ surface char, oper eae Jength 4 em when placed surfaces of the shells are opal “~~ with its axis making an angle of 60° with a Determine the ratio Q,:Q» Foraign 2013 uniform electric field, experiences a torque of ner a3 Nan. Calculate the potential energy of rE Ocilate the arenas a of “an sd the dipole, if it has charge + 8 nC. Dabhi enia moment 3x 10°* C - m from its position 21. An electric dipole of length 2 cm when placed of unstable equilibrium to the position with its axis making an angle of 60° with a of stable equilibrium in a uniform . uniform electric field, experiences a torque of electric field of intensity 10° NC. 8V3 N-m. Calculate the potential energy of Foretgn 207 the dipole if it has charge of + 4 nC. pethi 2014 28. Plot a graph showing the variation of 22. An electric dipole of length 1em when placed Sra force F versus W/r?, where ris wathitts exis meking an angle of 60° with a the distance between the two charges i . 5 i s id uniform electric field, experiences a torque of a eer Pel ot ca 6V3 N-m. Calculate the potential energy of 4 fag ad obtaified. All india 20n1c the dipole, if it has charge + 2 nC. bethi ee DM. “Two identical metallic spherical shells 23. An electric dipole is placed in a uniform Aand B having charges + 4@Q and electric field E with its dipole moment p —10Q are kept a certain distance parallel to the field. Find apart. A third identical uncharged @ the work done in turning the dipole till sphere C is first placed in contact with its dipole moment points in the direction sphere A and then with sphere B, then opposite to E. spheres A and B are brought in contact (ii) the orientation of the dipole for which and then separated. Find the charge the torque acting on it becomes on the spheres A and B. All india 201 maximum. All india 2014¢ 30. A dipole with a dipole moment of 24. A small metal sphere carrying a charge +Q is magnitude pis in stable equilibrium in located at the centre of a spherical cavity in a an electrostatic field of magnitude E. large uncharged metallic spherical shell. Find the work done in rotating this Write the charges on the inner and outer dipole to its position of unstable surfaces of the shell. Write the expression for equilibrium. all india 2010¢ the electric field at the point P,. Delhi zo1ac ~ A dipole is present in an electrostatic field of magnitude 10° NC™. If the work done in rotating it from its position of stable equilibrium to its position of unstable equilibrium is 2x 107° J, then find the magnitude of the dipole moment of this dipole. All india 20106 32. Detucy the expression for the electric 25. Point charge (+ @) is kept in the vicinity of an field Eat a pointr due to a system of . | two charges q, and @, with position uncharged conducting plate. Sketch electric caine and with “~ field lines between the charge and the platen. common origin. ee 93. Porce on positive charge due to electric fleld is always in the direction of electric field, So, proton being a positively charge will tend to move along he X-axis Le. in the direction of a uniform electric field, 0) 74 (i) Por stable equilibrium, the angle between p and E is 0° ic. it should be placed parallel to electric field, (v2) (ii) For unstable equilibrium, the angle between p and E is 180° ic. it should be placed antiparallel to electric field. +9 mad (72) 45. Two point charges system is taken from air to water keeping other variables (e.g. distance, magnitude of charge) unchanged. So, only factor which may affect the interacting force is dielectric constant of the medium. Force acting between two point charges in a medium is Fe! _ 42 4ne,K 7? or FFiee He K a => =K Fnediun = 8 280 Fyaer 8 — Fates = 30 1 = Fyater = — N eee NO m 16. Path d is followed by electric field lines because electric field intensity inside the metallic sphere will be zero. Therefore, no electric lines of force exist inside the sphere, Also electric field lines are ne to the surface of the a 17. Right, because mutual force acting between two point charges Is proportional to the product of magnitude of charges and inversely proportional to the square of the distance between them Le. independent of the other ¢ harges. o 18. Refer to text on page 5 (Torque on an electric dipole placed in a uniform electric fleld). a 19. (i) Electric fleld at a point on the equatorial line of an electric dipole. Consider an electric dipole consisting of t point charges + 4 and = q separated by a sna distance AB = 2/ with centre at O and dipol moment, p = q(21) as shown in the figure. Resultant electric field intensity at the point Q Ey = E, + Ey ee) 4mey (x? + 2) 1 and £,=——- Ane, Here, M On resolving E,andE, into two rectangular components, the vectors E,sin® and Ey sin@ are equal in magnitude and opposite to each other and hence, cancel out. The vectors E , cos@and E, cos@ are acting along the same direction and hence, add up. +, Eg = E, 0080 + Ey, cosd = 2B, cos nee q ! [: cos0 = ae (e os ri no al 4mey (x? + 2"? But, the dipole moment | p|= q x 2/ 1 . AN? jf eee Oa) (+ PE  ' “CHAPTER 1: Electric Charges and Fields aa Ct of The direction of E is along £4 that is parallel to 7 BA, i.e. opposite to AB. In vector form, we can Tewrite as, Ey =—___—P a ane (x? + PP? rm * 20. Given, t Length (2a) = 4cm = 4x 10m Loria) Angle, @ = 60° Torque, t = 4¥3 N-m of ty Charge, Q= 8 x 107°C | Sty We know that, t = Q(2a) E sin pg Electric field, F = —_* __ Q(2a)sin® Epo 43 8x10? x4 107 xsin 60° (yy E=2.5x10'°Nc"! -. Potential energy, U =—pEcos® =~ Q(2a) E cos0 U=- 8x10" x 4x 107 x 2.5x 10" cos 60° =-4J a 21. 16 J, Refer to Sol. 20 on page 11. (2) 22. 6 J, Refer to Sol. 20 on page 11 (2) ° ) 23. (i) Work done in rotating the dipole, W = J, td0 ) If the dipole is turned from direction parallel to electric field to direction opposite to electric field, then angle @ will change trom 0 to x. We Jiresino do= pe [-cos0]k = 2pE @ (ii) We know that, t = pEsin® : If @= n/2, then tis maximum | ad 5 ie. tT=pEsin— = t=pE (maximum) ie 2 F mM 24. According to the question, the charge on inner surface = — Q and the charge on outer surface = + Q Blectric field at point A is given by E = Q/4ney 1? (2) 25. Equal charge of opposite nature induces on the surface of conductor nearer to the source charge. 26. 27. 28. n Electric lines of forces should fall normally on the surface of conductor , i.e. at 90° on the conducting plate. (2) Surface charge density, gaat 4nR’ According to the question, surface charge density, 6 = constant las Let Q, and Q, are two charges Hence, Charge, Q, = 4nR’o -a(l) Charge, Q, = 4n(2R)’o (ii) On dividing Eq. (i) with Eq. (ii), we get Q_ 4nRo (1 Q 4xaR?o 4 ey According to question, for unstable equilibrium, the angle between p and E is ®@, =180° Finally, for stable equilibrium, @, = 0° (v2) Required work done W = pE(cos®, ~ cos®,) (V2) = 3x10 x10?(cos180° — cos0°) [+ cos] 80° = -1 and cos0° = +1] W=-6x10"J o According to Coulomb’s law, the magnitude of force acting between two stationary point charges GW 42 1 is given by #=[ 2 ( 7) 4ne, )\r? For given 4; 49, r=(4) r 1 The slope of F versus r graph depends on q, q. Magnitude of q, q, is higher for second pair. as graph corresponding to = second pair (1p.C, — 31C) is greater. Higher the magnitude of product of charges q, and q,, higher the slope. a) For (1 wC, -3 pC) pair of charges pat oa «. Slope of F versus force F —+ Magnitude of  contact, charge of A | two spheres. Therefore, charges cal shell A and C = + 2Q. oO sp d in contact with B, then charge shell B and C becomes A and B are placed in contact, then charge A and B becomes 20+ (49 __y 2 mM 30. For stable equilibrium, the angle between p and E : 6, =0°. For unstable equilibrium, 8, =180°. a) _ Work done in rotating the dipole from angle 8, 108, . W = pE(cos®, ~ cos0,) = pE(cos0° — cos180°) : W = 2pE 31. Electric field intensity, B =10° Nc“ » Work done, w = 2x 10°? J Work done in rotating the dipole from stable = equilibrium position 10 unstable equilibrium : position. a W = pE(cos®, ~ cos8,) W = pE (cos 0° — cos 180°) = 2pE a Magnitude of dipole moment is if WwW. a. am ” Seer ig 2x10° 32. Let two point charges g, and 92 are situated at yi (potas A and B have position vectors f and r,. y & 10° C-m mM «. Net electric field intensity at point E=E,+E, =| rane Ane | |r-¥| 33. (i) An electron falls through distance 1. electric field is 2x10* N/C. So, net force on electron F = 4,E m,a = 4q,E aa FE [- F = ma] m, where, g, = 1.6107 C, = 91107! kg and =E=2x10'N/C m 16x10"! x 2x104 SO, q2 _.._ 91x10! = 35x10" m/s? As we know, 5 = ut +! gf? iz So, 15x10? =0xr41y 35x 10! x (2 2 [2x1.5x10% (= _ 35x10" = V857x10 = 292ns (ii) Similarly, time of fall of proton if direction 9 field is reversed 251 I 4 Sie = — “ay = 4% Pp qp m, | where, m, =16x10°7 kg, % =16x10-%¢ ands =i.5cm a t, = |2%15x107 x16 x10 eee ee 1.6 x10" x 2x ]9% =ylsxio™