Electromagnetism | UNIT 4 iy ; Electrostatics, Current Electricity, Magnetic Effects of | Current, Magnetism, Electromagnetic Induction, | Alternating Currents, Electromagnetic Waves | Choose the correct answer : 4. Six point charges (each of magnitude Q) are placed on the six vertices of a cube of side x, (1) 2, rgmd® | eegmd? such that two adjacent vertices are vacant. ah a Electrostatic field intensity at the centre of the z z 1 lane ymd’ 2negmd’ oe 2n, (4) nfo cube is (« x) @) 2 ) a 42 kQ . 8y2 1a A block of mass m having positive charge q is BF 2) SB x placed on smooth horizontal floor. A horizontal electric field is switched on at f = 0. If coefficient of v2 kQ 4) 4x2 ka 1 ® 38 2 (4) ova restitution is >, then total distance travelled by the A uniform electric field E is created between two bald parallel plates as shown in figure. A charge (q, m) enters the field between the plates with speed, V,, E If the length of each plate is J, then the angle of afm deviation in path of charge particle as it comes out of field is ype _ vs 4 o> @) 20 -4(_gEe +( aEe eal tant] Er sin] SEO @) 3d «@ o (2%) @ mye : 5. Electric field at point P(x, y) makes an angle o (se) (He) Gi 7) with positive x-axis. Equation of electric 3. Two infinite line charges having linear charge density +2, are placed at distance 2d. A negative charge particle (-q, m) is kept at mid point between the two line charges on giving slight (1) displacement in plane perpendicular to the plane of rod, charge particle performs SHM with time period, T. Value of Tis @) field lines may be constant (2) 2+ ¥ = constant =constant (4) y? — x? = constant SY, E Corporate Office 1 Aakash Tower, 8, Pusa Road, New Delhi-110005. Phono : 011-47623456= 86 Electromagnetism ‘Success Achiever A charge q is fixed at the centre of a quarter 10. A point charge q is placed at origin. Find the circular ring (of radius r and linear charge fh the hemispherical reglor density 2). The space is gravity free and the ring aes fux through te beree! on is held in position by two threads as shown. (x- Ba) +y? +2? =2", x> 3a Tension in thread-1 is (« ea } q q ane 0a @) 25 Thread-t (Insulating) 1 q Hf 22-8 oX-e) oa) 11. Two isolated large metal plates are charged to charge densities + o and ~ o respectively. Now they are brought close together to form a parallel plate capacitor. Electrostatic pressure experienced by each of the plates is RK @) 34 of ot oe ae 2K. : : 24, A i a) (4 20° 4o’ @ a @ o # o Which of these can be electrostatic ld function? 4» Consider a systam of four large thin metal plates (1) Qxy f+ x27 (2) x? F+2xyj (of plate area A each), arranged parallel to each other Bue aoe as shown, in steady state. Now the key is closed, (3) xj+yk 4) xtjtyk ‘so that the system again reaches steady state. ‘A point charge -9 (of mass m) is revolving in a Work done by the call, after the key is closed, is circle of radius r, around a long positive line of charge with charge density 2, as shown in diagram. Its angular frequency is (« 2€ AV? eg AV? Sa @ Sg ep AV? @ 2y- (4) Zero 19, There are ninfinite metal plates arranged parallel to each other as shown. Q,, Q,, Qs... Q, are a respective charges on these plates. Charge Q on “ 2ka%. @ the left surface of leftmost plate in the arrangement is me me Of 0) OQ: Q, p. kgh. “SF of Ati-t Consider a system of three concentric metallic shells of radii r, 2r and 3r carrying charges q,, 4 and q, respectively. Potential difference between the innermost and the outermost shell does not depend on (3) Zero ) a Qa (4) Indeterminate, as distances between different (3) 95 @r plates are not giveney "pine Z steady stat youit shown is in steady state, Electro tre ar eneray stored by the circuits int pole! fe 2c 4c R — ¢ Vv R 3cR OR We () a 3 cv 8" ® rev" [JEE (Main)-2018] parallel plate capacitor of capacitance 90 pF ig connected to a baltery of emf 20 V. Ifa Gelectric material of dielectric constant is inserted between the plates, the magritude of the induced charge will be (ty 12nC @) 03nc @) 24nc @) 09nc {g. Two long parallel wires having linear charge density are placed along z-axis passes through 0, 0) and (a, 0,0). Maximum magnitude of gedti¢ field at a point on y-axis is ee a * AR - ) aga @ Freee 2 © ia @) ea 16 Adielectric material slab of relative permittivity 3 is placed in a uniform electric field E, i. Electric field inside the dielectric due to polarisation is . oo y 7 @ ai 8) = (4) Corporate Office : Aakash Tower, 8, Pusa Road, 18, 19, Electromagnetism 87 A dipole of dipole moment p is placed at distance d from a point charge Q. Force of interaction between charge particle and dipole is Q : ee —— 20p 2) eg Op @) “reqa? The electric field (E) and potential (V) due to the Vv field are related as E = a For the V vs r graph shown, identify the correct E vs r graph HK. =“ Consider a uniform solid sphere of charge Q and radius R. What is the electrostatic potential energy stored in the region O R, where ris the distance from the origin, The electric field at a distance (r < R) from the origin is given by Anper (5 @) 3c, G 4) wo=n(é 4) upto r= R, and p(r) = 0 [VEE (Main)-2016] 20d. The region between two concentric spheres of radii ‘a’ and ‘b’, respectively (see figure), has volume charge densily p=“, where Ais a r constant and ris the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the lect field in the region between the sj will be constant, is Be c, Ny (AIEEE 2012) In a uniformly charged sphere of yy Qand radius R, the electric feld ha as a function of distance from the oh Prot, graph which would correspond tg ate Ty will be : 8 ay 20c. a t 21. A quantity V depends on ras Here, K, Q and R are (+ve) constant. Which the following graph represents the variation ff ay with r? “4 + “ ei +r =., Y v §) IN. “ Corporate Office : 0: Aakash Towor, 8, Pusa Road, Now Dolhi-110005, Phono : 011-47623456suc 2 ‘ess Achiever ‘a shott dipole of dipole moment the centre of a spherical cavi spher? as Shown. Electric ent pj is placed at iy inside a solid metal field Shown on the x-axis) due to charges ote (88 the surfaces of the metal sph charges induced on ere is 2a. [JEE (Main)-2020] Consider a sphere of radius R which carries a uniform charge density p. If a sphere of R. radius > is carved out of it, as shown, the 1Eal - _ ratio FE Of magnitude of electric field Ey and Eg, respectively, at points A and B due to the remaining portion is: 23. 24, 25. 89 Electromagnetism Electrostatic potential in a region is given by (ey - =| For which of the following positions of a point charge, only x-component of force experienced by the charge is zero? (1) (0, 0, 0) @ (0.2.2) @) (2,0,2) (4) (2, 2,0) The electric field on two sides of charged non conducting sheet is shown in figure. The surface charge density on plate is E, E, (1) e9(E, - E,) (2) eg(E + Ey) @) &(E,-2E,) (8) e((E, ~ 2E)) Consider the cube shown. A point charge 8q is placed at a vertex G of the cube and another charge 4q is placed at the centre of an edge AE of the cube. Electric flux through the cube is a8 ay a c D G H 8q q 2q a 2 24 2 a 3 @ 2 (@) Ze % Consider a parallel plate capacitor connected across the terminals of a battery. Now a dielectric slab (of dielectric constant k) is introduced in between the plates so as to completely fil in the space between the plates. New value of electrostatic energy in steady state is (1) k times 2 tines (3) Same as earlior value (4) Infinite Corporate Office : Aakash Towor, 8, Pusa Road, Naw Dalhi-110005, Phona : 011-4762345690" Electromagnetism 27. The equivalent capacitance of the arrangement across A and Bis c © Tg ¢ 8 c c a 3e @) 2 12, @) ze @ +e 28. Space between plates of a parallel plate capacitor is filled with three dielectric slabs as shown. Equivalent dielectric constant for the arrangement shown (between points X and Y) is rez 3 (2) 6 @) 9 (4) 12 29. Equipotential surfaces corresponding to a uniform electric field are (1) Straight lines (2) Planar 8) Spherical (4) Ellipsoidal 30. A point charge q is placed at the vertex of a cone with height 12 cm and radius § cm. Electric flux through the base of the cone is 4 ae Fe, © ie ae q ©) FBe5 ® Fees 31. Two points A and B are maintained at the potentials 20 V and -5 V respectively. The work done in moving 50 electrons from A to B will be (2) 2x 10-6 J (4) -2 « 10-18 y (1) 3 * 10-16 J (3) -3« 10% J Suc0888 Ay, A charged particle (of charge q and my " projected between plates of a arash capacitor a8 shown, at t= 0. Time! Oy instantaneous power delivered by the gj Mig to the particle is zero is tic to ., Trajectoy ~ of the partis =o (Plate Area = A) 2mueg sina 5 muta sina ( m5 mueo sina. 290 mug sine. 4qo 4) [JEE (Main)-2020} 32a, A particle of mass m and charge qisreleasy from rest in a uniform electric fed. I thereig no other force on the particle, the dependence ofits speed v on the distance x travelled bya is correctly given by (graphs are schematic ang not drawn to scale) (a) Corporato Office : Aakash Towor, 8, Pusa Road, Naw Doihl-110005, Phono : 014-47623458‘achiever wt mich of these May De representin, 19 elect. 3 fd tines? static 34, o Metallic sheet aq Metal plate —— @_, 35. = [JEE (Main)-2015} ga. Along cylindrical shell carries positive surface charge in the upper half and negative surface charge —o in the lower half. The electric field lines around the cylinder will look lke figure given in (figures are schematic and rnot drawn fo scale) Electromagnetism [191 il For an arrangement of six identical capacitors ‘shown here, terminals of various capacitors have been marked. Between which two points should a battery be connected so that each of the capacitors gets charged? gag Se u (1) Between P and U (2) Between T and S (3) Between R and U (4) Itis not possible to charge all the capacitors by connecting battery across any two marked points A solid metal ball (with radius r, and charge q,) is Surrounded by a metallic shell (with radius r, and charge q,), as shown. If the key is now closed final charge and potential of the ball respectively are. %. key Ge () 0, 1 uta) mE 2) 0, 1 (ata) any +92 1 (+42) Be tag Gh+ere 1 (a+42) Ont | at htt ' Antg hy Consider four point charges placed on the vertices of a square (of side x) as shown. Electric dipole moment of the system is -Q,_ * 29 x tL. @-J2)q -@ (1) (W2-1)ax (i+}) 8) W2-Aax (7 @ W2+Hax +) D @) W2+1 ax ij)37. Three concentric metal shells A, 8 and C of respective radii a, b and c (a < b < c) have surface charge densities a4, % and Ge respectively. The potential of shell B is 1 (1) -e(aa4 + bo + 600) @) 2{on+snseve) ol > H(t 0) 2 {Bont M oor toe # “ 2 (ors t04+ Za} 38. Consider a system of two short dipoles placed along x-axis at a separation d. Force on dipole with dipole moment p due tothe ater dite I 3p? 3p " 1 attractive (2) + repulsive () oe @ ee 3p? i 3p? ; see Seaa* repul ©) Frege" tractive (8) 3 repulsive 39. Consider a system of two small conducting spheres (of radius r each) separated by a large distance. Capacitance of the arrangement is. (1) ey (2) 2m 3) amy 4) Brey 40. Two point charges q and ~29 are fixed at distance 30 from each other. Radius of the sphere of points in space where potential is zero is ja (2) 2d @) 34 (4) 4a 41. Point charge Q is placed out-side a conducting sphere as shown in Fig. The olectric field at tho centre O due to induced charges upon sphoro will bo where k=—1_ Frey a; a ka) Qk Soy a) k Zui) @) hea @) 2a 42. A parallel plato capacitor is charg battery. The force (electrostatic) or ao, between plates is E,. Now a dielet relative permittivity ¢, is introduce boty plates so as to fill the spac 8. The et electrostatic attraction be ° a ion becomes E,. Then [Note : The battery remains «, on insertion of stab] eM he E 4) E, =F (1) & @ Qe @ Feat [JEE (Main)-2014) 42a. A parallel plate capacitor is made of tre circular plates separated by a distance 5 mn and with a dielectric of dielectric constant 22 between them. When the electric fied inte dielectric is 3 x 10 Vim, the charge dersty of the positive plate will be close to (1) 6 x 1077 Gim? (2) 3x 107 Cim? (3) 3x 108 cim? (4) 6 x 108 Cim? Corporate Office : Aakash Towor, 8, Pus Road, New Dolhl-110005, Phone : 01147623458a noone sider # sySt0M Of WO Uniform, thin, concentra 46. 5 Om onducting shells of charge with respects 12 ges Q and ~20 and radii R and 3R. A pory @ 40 is placed at a distance SR from tne ertirancente of he shell. Net force experianeng oom ute shell by 20 2 28 ae 28negR? 20° (4) Zero 2a © SreoR® metal ing ("adius R) is uniformly charged with A Haige ©. Asmmall element of angular width ab ig Gurout. The electric field at centre © due to 47. ‘na will be nko : residual charged ring will be ">. Where —— ]. Find the lue of ‘n’, tro y.axis (i a OW Ole 33 $j of), 5. Charge Cis divided into two parts C, and C, such that when these parts are placed at a distance d fom each other in air, they repel with maximum force. Then c =e =F 7 c 2c 2 Gas Cyan 3 c 3c e=2,¢, =32 0) = 2.0 = 3c c # G=%.c, -& le Electromagnetism | 93 Three charges are placed at the comers of an equilateral triangle of side J, The dipole moment of the system is 23 git + yj). Then ANG B. Cc ~2q q () x24, yas Q) xety=t @ x=B.y ) x=4y=4 ‘A short dipole of dipole moment A is placed at distance x from origin. A charge Q is kept fixed at origin. The force (electric) upon electric dipole due to point-charge Q, will be Fixed la. P charge xa x Short dipole 1 PQ,- 1_(2PQ)\, 3, O Fee Ome) 1_(2PQ),- 1 (PQ), 5 @ wel) o ame]? ‘A point charge (m, q) is placed at rest at point X at distance r from a short electric dipole. The initial kap acceleration of charge a=—2n where 2mr' 1 ‘4ne, - Then nis BY (short electric dipole) (1) VB @ v7 @) ve (4) 2 Corporate Office : Aakash Tower, 8, Pusa Road, New Delhi-110005. Phone : 011-4762345694 Electromagnetism [JEE (Main)-2017] t 48a. An clectric dipole has a fixed dipole notes B, which makes angle 0 with respect ia xeaxis, When subjected to an electric fie Ey Ei ue Ti E;=€/, it experiences a torq When subjected to another electric field V3E,j it experionces a torque eth. E, Fz =-F,. The angle 0 is (1) 6" (2) 90° @B) 30° (4) 45° 49. A point charge (m, q) moves with constant velocity V towards uncharged but earthed conductor. The current that flows from conductor to earth at the instant shown is uncharged spherical conductor av Ma aR’v @ @ x st. gRv? 3 @) re (4) Zero [JEE (Main)-2014] 49a. Assume that an electric field E= 30x77 exists in space. Then the potential difference V, — Vo, where Vo is the potential at the | 52, origin and V, the potential at x = 2 mis 1204 -120J 80 J e80J q) 2) @) 4) 50. Consider a system of two point charges Q and -30 placed at (0, -a) and (0, a) respectively. Which of the following graphs shows variation of electric potential (V) with y-coordinate (y) for any point on y-axis? Three identical metallic spheres A, B an, given charges 32 C, 16 C and 8 C respecp. Now A and are brought in contac, then 8 and then & A. The final charges on the ssh A, Band C respectively are Cay (1) 24C,24C,8C — @) 206, 18c,20¢ (4) 24, 86,240 ‘A spherical capacitor of radii a and b (>) te capacitance C, when inner sphere is charged ar: @) 16, 24¢, 16C outer is earthed. Its capacitance is C,, when oz sphere is charged and inner is uncharged ft earthed. Then () C=, ab @) C=C.e4ro @) C= C+ dnegb (4) C, = C,—4negb Corporate Office : Aakash Towor, 8, Pusa Road, Now Delhi-110005, Phone : 011-47629456