Gauss's Law PYQs Set 3 (PDF)

Set 3 of 4 · Questions 61-90 of 113

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Mere Teacher · Previous Year Questions JEE Main Physics · Gauss's Law · Set 3 (Q61-90)
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61. $An infinitely long thin straight wire has uniform linear charge density of \frac{1}{3} Cm^{- 1} . Then the magnitude of the force acting on a charge 3 μC situated at a point of 18 cm away from the wire is (\frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} Nm^{2} C^{- 2})$ (1) $2 \times 10^{5} N$ (2) $10^{5} N$ (3) $\frac{1}{3} \times 10^{6} N$ (4) $3 \times 10^{11} N$ 62. $Two parallel infinite line charges with linear charge densities + λC / m and - λC / m are placed at a distance of 2R in free space. What is the electric field mid‐way between the two line charges?$ (1) $\frac{λ}{2 π ϵ _{0} R} N / C$ (2) $zero$ (3) $\frac{2 λ}{π ϵ _{0} R} N / C$ (4) $\frac{λ}{π ϵ _{0} R} N / C$ 63. $Four closed surfaces S_{1}, S_{2}, S_{3} and S_{4} together with charges + q, - q and -2q are shown. Through which one of the surfaces the net flux is zero?$ (1) $S_{1}$ (2) $S_{2}$ (3) $S_{3}$ (4) $S_{4}$ 64. $Two tiny spheres carrying charges 1.8 μC and 2.8 μC are located at 40 cm apart. The potential at the mid-point of the line joining the two charges is$ (1) $4.3 \times 10^{4} V$ (2) $3.8 \times 10^{4} V$ (3) $3.6 \times 10^{5} V$ (4) $2.1 \times 10^{5} V$ 65. $Two charged identical metal spheres A and B repel each other with a force of 3 \times 10^{- 5} N . Another identical uncharged sphere C is touched with sphere A and then it is placed mid-way between A and B. Then, the magnitude of net force on C is$ (1) $1 \times 10^{- 5} N$ (2) $3 \times 10^{- 5} N$ (3) $2 \times 10^{- 5} N$ (4) $5 \times 10^{- 5} N$ 66. $Three charges, each +q, are placed at the corners of an isosceles triangle ABC of sides BC and AC, 2 a . D and E are the mid points of BC and CA. The work done in taking a charge Q from D to E is$ (1) $\frac{3 qQ}{4 π ϵ _{0} a}$ (2) $\frac{3 qQ}{8 π ϵ _{0} a}$ (3) $\frac{qQ}{4 π ϵ _{0} a}$ (4) $zero$ 67. $Two identical charged spheres suspended from a common point by two mass less strings of lengths l, are initially at a distance d(d << l) a part because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then v varies as a function of the distance x between the spheres, as:$ (1) $v µ x^{-1}$ (2) $v µ x^{1/2}$ (3) $v µ x$ (4) $v µ x^{-1/2}$ 68. $What is the electric flux for Gaussian surface A that encloses the charged particles in free space? (Given, q_{1} = - 14 nC, q_{2} = 78.85 nC, q_{3} = - 56 nC)]$ (1) $10^{3} N - m^{2} C^{- 1}$ (2) $10^{3} C - N^{- 1} m^{- 2}$ (3) $632 \times 10^{3} N - m^{2} C^{- 1}$ (4) $632\times103C-N-1 m^{- 2}$ 69. $What is the flux through a cube of side 'a' if a point charge of q is at one of its corner$ (1) $\frac{2 q}{ϵ _{0}}$ (2) $\frac{q}{8 ϵ _{0}}$ (3) $\frac{q}{ϵ _{0}}$ (4) $\frac{q}{2 ϵ _{0}} 6 a^{2}$ 70. $The given figure gives electric lines of force due to two charges q_{1} and q_{2} . What are the signs of the two charges?$ (1) $q_{1} is positive but q_{2} is negative$ (2) $q_{1} is negative but q_{2} is positive$ (3) $both are negative$ (4) $both are positive.$ 71. $Two electrons each are fixed at a distance '2d'. A third charge proton placed at the midpoint is displaced slightly by a distance x (x << d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency: (m = mass of charged particle)$ (1) $(\frac{q ^{2}}{2 π ϵ _{0} m d ^{3}})^{\frac{1}{2}}$ (2) $(\frac{π ϵ _{0} m d ^{3}}{2 q ^{2}})^{\frac{1}{2}}$ (3) $(\frac{2 π ϵ _{0} m d ^{3}}{q ^{2}})^{\frac{1}{2}}$ (4) $(\frac{2 q ^{2}}{2 π ϵ _{0} m d ^{3}})^{\frac{1}{2}}$ 72. $A positive point charge is released from rest at a distance r_{0} from a positive line charge with uniform density. The speed (v) of the point charge, as a function of instantaneous distance r from line charge, is proportional to$ (1) $v \propto e^{+ \frac{r}{r _{0}}}$ (2) $v \propto ln (\frac{r}{r _{0}})$ (3) $v \propto ln (\frac{r}{r _{0}})$ (4) $v \propto (\frac{r}{r _{0}})$ 73. $Three charges +Q, q, +Q are placed respectively, at distance d/2 and d from the origin, on the x-axis. If the net force experienced by +Q, placed at x = 0, is zero, then value of q is:$ (1) $- Q /4$ (2) $+ Q /2$ (3) $+ Q /4$ (4) $- Q /2$ 74. $Suppose the charge of a proton and an electron differ slightly One of them is -e, the other is (e + Δ e) . If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δ e is of the order of [Given: mass of hydrogen m_{h} = 1.67 \times 1 0^{- 27} kg]$ (1) $1 0^{- 23} C$ (2) $1 0^{- 37} C$ (3) $1 0^{- 47} C$ (4) $1 0^{- 20} C$ 75. $Three charges 4 q, Q and q are placed at positions 0, \frac{l}{2} and l respectively along a straight line. If the resultant force on q is zero, then Q is equal to$ (1) $-q$ (2) $-2q$ (3) $- \frac{q}{2}$ (4) $4qt$ 76. $A cube is placed inside an electric field, E = 150 y^{2} j . The side of the cube 0.5m is and is placed in the field as shown in the given figure. The charge inside the cube is:$ (1) $3.8 \times 1 0^{- 11} C$ (2) $8.3 \times 1 0^{- 11} C$ (3) $3.8 \times 1 0^{- 12} C$ (4) $8.3 \times 1 0^{- 12} C$ 77. $Two parallel infinite line charges with linear charge densities +λ C/m and -λ C/m are placed at a distance of 2R in free space. What is the electric field mid-way between the two line charges?$ (1) $\frac{λ}{2 π ε _{0} R} N / C$ (2) $zero$ (3) $\frac{2 λ}{π ε _{0} R} N / C$ (4) $\frac{λ}{π ε _{0} R} N / C$ 78. $A charge q is placed at the centre of the line joining two equal charges Q. The system of the three charges will be in equilibrium if q is equal to$ (1) $- Q /4$ (2) $Q/4$ (3) $- Q /2$ (4) $Q/2$ 79. $The given graph shows variation (with distance r from center) of:$ (1) $Electric field of a uniformly charged sphere$ (2) $Potential of a uniformly charged spherical shell$ (3) $Potential of a uniformly charged sphere$ (4) $Electric field of uniformly charged spherical shell$ 80. $Consider the charged cylindrical capacitor. The magnitude of electric field E in its annual region$ (1) $varies as \frac{1}{r}, where r is the distance from its axis.$ (2) $is zero.$ (3) $is same throughout and \| E \| > 0 .$ (4) $varies as \frac{1}{r ^{2}}, where r is the distance from its axis.$ 81. $Shown in figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q. At its centre is a dipole P as shown. In this case:$ (1) $Surface charge density on the inner surface is uniform and equal to$ (2) $Electric field outside the shell is the same as that of a point charge at the center of the shell.$ (3) $Surface charge density on the outer surface depends on P .$ (4) $Surface charge density on the inner surface of the shell is zero everywhere.$ 82. $The variation of electrostatic potential with radial distance r from the center of a positively charged metallic thin shell of radius R is given by the graph [NEET 2020]$ (1) (2) (3) (4) 83. $Three charges of each magnitude 100 μC are placed at the corners A, B and C of an equilateral triangle of side 4 m. If the charges at points A and C are positive and the charge at point B is negative, then the magnitude of total force acting on the charge at C and angle made by it with AC are$ (1) $5.625 N, 60^{\circ}$ (2) $0.5625 N, 60^{\circ}$ (3) $5.625 N, 30^{\circ}$ (4) $0.5625 N, 30^{\circ}$ 84. $There is a uniform spherically symmetric surface charge density at a distance R_{0} from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V(R(t)) of the distribution as a function of its instantaneous radius R(t) is:$ (1) (2) (3) (4) 85. $Two metal spheres of radii 0.01 m and 0.02 m are given a charge of 15 mC and 45 mC respectively. They are then connected by a wire. The final charge on the first sphere is \times 10^{- 3} C .$ (1) $40$ (2) $30$ (3) $20$ (4) $10$ 86. $Two magnetic dipoles X and Y are placed at a separation d, with their axes perpendicular to each other. The dipole moment of Y is twice that of X. A particle of charge q is passing, through their midpoint P, at angle θ = 45° with the horizontal line, as shown in figure. What would be the magnitude of force on the particle at that instant? (d is much larger than the dimensions of the dipole)$ (1) $(\frac{μ _{0}}{4 π}) \frac{M}{( \frac{d}{2} ) ^{3}} \times qv$ (2) $0$ (3) $2 (\frac{μ _{0}}{4 π}) \frac{M}{( \frac{d}{2} ) ^{3}} \times qv$ (4) $(\frac{μ _{0}}{4 π}) \frac{2 M}{( \frac{d}{2} ) ^{3}} \times qv$ 87. $A cubical Gaussian surface has side of length a = 10 cm . Electric field lines are parallel to x axis as shown. The magnitudes of electric fields through surfaces ABCD z and EFGH are 6 kNC^{- 1} and 9 kNC^{- 1} respectively. Then, the total charge enclosed by the cube is [Take ϵ_{0} = 9 \times 10^{- 12} F m^{- 1}]$ (1) $- 0.27 nC$ (2) $1.35 nC$ (3) $- 1.35 nC$ (4) $0.27 nC$ 88. $A large metal plate has a surface charge density of 8.85 \times 10^{- 6} C / m^{2} . An electron having initial kinetic energy of 8 \times 10^{- 17} J is moving towards the center of the plate. If the electron stops just before reaching the plate then the initial distance between the electron and the plate is [Take ϵ_{0} = 8.85 \times 10^{- 12} C^{2} / Nm^{2}]$ (1) $0.5 mm$ (2) $0.1 mm$ (3) $0.2 mm$ (4) $None$ 89. $Two small spheres each of mass 10 mg are suspended from a point by threads 0.5 m long. They are equally charged and repel each other to a distance of 0.20 m. Then charge on each of the sphere is \frac{a}{21} \times 1 0^{- 8} C . The value of 'a' will be:$ 90. $Two identical conducting spheres with negligible volume have 2.1nC and -0.1nC charges, respectively. They are brought into contact and then separated by a distance of 0.5m. The electrostatic force acting between the spheres is ____\times 10^{- 9} N [Given: 4 π ϵ_{0} = \frac{1}{9 \times 10 ^{9}} SI Unit]$