Electrostatics PYQs Set 4 (PDF)

Set 4 of 12 · Questions 91-120 of 349

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Mere Teacher · Previous Year Questions NEET Physics · Electrostatics · Set 4 (Q91-120)
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91. $A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is$ (1) $\frac{1}{2} ϵ_{0} E^{2}$ (2) $\frac{E ^{2} Ad}{ϵ _{0}}$ (3) $\frac{1}{2} ϵ_{0} E^{2} Ad$ (4) $ϵ_{0} EAd$ 92. $The electrostatic potential inside a charged sphere is given as V = A r^{2} + B, where r is the distance from the center of the sphere, A and B are constants. Then, the charge density in the sphere is$ (1) $16 A ϵ_{0}$ (2) $- 6 A ϵ_{0}$ (3) $20 A ϵ_{0}$ (4) $- 15 A ϵ_{0}$ 93. $Two point charges - 4 μc and 4 μc, constituting an electric dipole, are placed at (- 9, 0, 0) cm and (9, 0, 0) cm in a uniform electric field of strength 10^{4} NC^{- 1} . The work done on the dipole in rotating it from the equilibrium through 180^{\circ} is:$ (1) $18.4 mJ$ (2) $14.4 mJ$ (3) $12.4 mJ$ (4) $16.4 mJ$ 94. $Electric field at a distance r from an infinitely long uniformly charged straight conductor, having linear charge density λ is E_{1} . Another uniformly charged conductor having same linear charge density λ is bent into a semicircle of radius r. The electric field at its center is E_{2} . Then$ (1) $E_{2} = πr E_{1}$ (2) $E_{2} = \frac{E _{1}}{r}$ (3) $E_{1} = E_{2}$ (4) $E_{1} = πr E_{2}$ 95. $If \oint E \cdot dS = 0 over a surface, then [NEET 2023]$ (1) $the magnitude of electric field on the surface is constant.$ (2) $all the charges must necessarily be inside the surface.$ (3) $the electric field inside the surface is necessarily uniform.$ (4) $the number of flux lines entering the surface must be equal to the number of flux lines leaving it.$ 96. $If E_{a} and E_{q} represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance ' r ' from the centre of the dipole, then$ (1) $E_{a} = E_{q}$ (2) $E_{a} = \frac{1}{2} E_{q}$ (3) $E_{a} = \frac{1}{2} E_{q}$ (4) $E_{a} = 2 E_{q}$ 97. $The electrostatic potential due to an electric dipole at a distance ' r ' varies as:$ (1) $r$ (2) $\frac{1}{r ^{2}}$ (3) $\frac{1}{r ^{3}}$ (4) $\frac{1}{r}$ 98. $A List I A. Gauss’s Law in Electrostatics B. Faraday’s Law C. Gauss’s Law in Magnetism D. Ampere Maxwell Law Lost II I. \oint E \cdot d l = - \frac{d φ _{B}}{dt} II. \oint B . d A = 0 III. \oint B . d l = μ_{0} i_{C} + μ_{0} \in_{0} \frac{d φ _{E}}{dt} IV. \oint E . d s = \frac{q}{ϵ _{0}} Choose the correct answer from the options given below:$ (1) $A-IV,B-I, C-II, D-III$ (2) $A-I, B-II, C-III, D-IV$ (3) $A-III, B-IV, C-I, D-II$ (4) $A-II, B-III, C-IV, D-I$ 99. $A simple pendulum with a bob of mass 40 g and charge + 2 μC makes 20 oscillation in 44 s . A vertical electric field magnitude 4.2 \times 10^{4} NC^{- 1} pointing downward is applied. The time taken by the pendulum to make 15 oscillation in the electric field is (acceleration due to gravity = 10 ms^{- 2})$ (1) $30 s$ (2) $60 s$ (3) $90 s$ (4) $15 s$ 100. $In a region, the potential is represented by V (x, y, z) = 6 x - 8 xy - 8 y + 6 yz, where V is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is$ (1) $65 N$ (2) $30 N$ (3) $24 N$ (4) $435 N$ 101. $A point dipole p = - p_{0} x kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively: (Take V = 0 at infinity)$ (1) $\frac{( p )}{4 π ϵ _{0} d ^{2}}, \frac{p}{4 π ϵ _{0} d ^{3}}$ (2) $0, - \frac{p}{4 π ϵ _{0} d ^{3}}$ (3) $0, \frac{p}{4 π ϵ _{0} d ^{3}}$ (4) $\frac{( p )}{4 π ϵ _{0} d ^{2}}, \frac{- p}{4 π ϵ _{0} d ^{3}}$ 102. $Two point charges + 8 μC and + 12 μC repel each other with a force of 48 N . When an additional charge of - 10 μC is given to each of these charges (the distance between the charges is unaltered) then the new force is$ (1) $repulsive force of 24 N$ (2) $attractive force of 24 N$ (3) $repulsive force of 12 N$ (4) $attractive force of 2 N$ 103. $A point charge +q is placed at the centre of a cube of side l. The electric flux emerging from the cube is$ (1) $\frac{6 q l ^{2}}{ϵ _{0}}$ (2) $\frac{q}{6 l ^{2_{8_{0}}}}$ (3) $zero$ (4) $\frac{q}{ϵ _{0}} .$ 104. $Ratio of thermal energy released in two resistor R and 3R connected in parallel in an electric circuit is:$ (1) $3 : 1$ (2) $1 : 1$ (3) $1 : 3$ (4) $1 : 27$ 105. $The electric potential at a point in free space due to charge Q coulomb is Q \times 1 0^{11} volts. The electric field at that point is$ (1) $4 π ϵ_{0} Q \times 1 0^{20} volt / m$ (2) $12 π ϵ_{0} Q \times 1 0^{22} volt / m$ (3) $4 π ϵ_{0} Q \times 1 0^{22} volt / m$ (4) $12 π ϵ_{0} Q \times 1 0^{20} volt / m$ 106. $Two equal and opposite charges of masses m_{1} and m_{2} are accelerated in an uniform electric field through the same distance. What is the ratio of their accelerations if their ratio of masses is \frac{m _{1}}{m _{2}} = 0.5 ?$ (1) $\frac{a _{1}}{a _{2}} = 2$ (2) $\frac{a _{1}}{a _{2}} = 0.5$ (3) $\frac{a _{1}}{a _{2}} = 3$ (4) $\frac{a _{1}}{a _{2}} = 1$ 107. $The electric potential at a point (x, y, z) is given by V = - x^{2} y - x z^{3} + 4 . The electric field at that point is$ (1) $E = i 2 xy + j (x^{2} + y^{2}) + k (3 xz - y^{2})$ (2) $E = i z^{3} + j xyz + k z^{2}$ (3) $E = i (2 xy - z^{3}) + j x y^{2} + k 3 z^{2} x$ (4) $E = i (2 xy + z^{3}) + j x^{2} + k 3 x z^{2}$ 108. $In a certain region of space with volume 0.2 m^{3}, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is [NEET 2020]$ (1) $0.5 N / C$ (2) $1 N / C$ (3) $5 N / C$ (4) $zero$ 109. $An electric dipole is kept in non-uniform electric field. It generally experiences$ (1) $A torque but not a force$ (2) $A force and torque$ (3) $Neither a force nor a torque$ (4) $A force but not a torque.$ 110. $Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :$ (1) $3^{2/3} : 1$ (2) $1 : 2^{2/3}$ (3) $1 : 3^{2/3}$ (4) $1 : 3^{1/3}$ 111. $An electric charge 10^{- 6} μC is placed at origin (0, 0) m of X - Y co-ordinate system. Two points P and Q are situated at (3, 3) m and (6, 0) m respectively. The potential difference between the points P and Q will be:$ (1) $3 V$ (2) $6 V$ (3) $0 V$ (4) $3 V$ 112. $An electric dipole is placed at an angle of 30^{\circ} with an electric field of intensity 2 \times 10^{5} NC^{- 1} . It experiences a torque equal to 4 N m. Calculate the magnitude of charge on the dipole, if the dipole length is 2 cm. [NEET 2023, 2016]$ (1) $6 mC$ (2) $4 mC$ (3) $2 mC$ (4) $8 mC$ 113. $Point charges + 4 q, - q and + 4 q are kept on the X ‐axis at point x = 0, x = a and x = 2 a respectively. Then$ (1) $only - q is in stable equilibrium$ (2) $all the charges are in stable equilibrium$ (3) $all of the charges are in unstable equilibrium$ (4) $none of the charges is in equilibrium$ 114. $A particle of mass m and charge q is in an electric and magnetic field given by E = 2 i + 3 j; B = 4 i + 6 j . The charged particle shifted from the origin to the point P (x = 1; y = 1) along a straight path. The magnitude of the total work done is:$ (1) $(0.35) q$ (2) $5q$ (3) $(2.5) q$ (4) $(0.15) q$ 115. $An electric dipole is formed by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency ω is:-$ (1) $\frac{qE}{md}$ (2) $\frac{2 qE}{md}$ (3) $2 \frac{qE}{md}$ (4) $\frac{qE}{2 md}$ 116. $The top of the atmosphere is at about 400 kV with respect to the surface of the earth, corresponding to an electric field that decreases with altitude. Near the surface of the earth, the field is about 100 V m^{- 1} . Still, we do not get an electric shock as we step out of our house into the open house because (assume the house to be a steel cage so that there is no field inside)$ (1) $there is a potential difference between our body and the ground$ (2) $100 V m^{- 1} is not a high electric field so that we do not feel the shock$ (3) $our body and the ground forms an equipotential surface$ (4) $the atmosphere is not a conductor.$ 117. $In a region the potential is represented by V(x, y, z) = 6x - 8xy -8y + 6yz, where V is in volts and x, y, z, are in meters. The electric force experienced by a charge of 2 coulomb situated at point (1, 1,1) is:$ (1) $65 N$ (2) $30N$ (3) $24N$ (4) $435 N$ 118. $Two opposite charges each of the magnitude 500 μC are 10 cm apart. Find electric field intensity at a distance of 25 cm from the midpoint on axial line of the dipole.$ (1) $5.76 \times 10^{7} NC^{- 1}$ (2) $9.28 \times 10^{7} NC^{- 1}$ (3) $13.1 \times 10^{10} NC^{- 1}$ (4) $20.5 \times 10^{7} NC^{- 1}$ 119. $Three infinitely long wires with linear charge density λ are placed along the x - axis, y axis and z-axis respectively. Which of the following denotes an equipotential surface?$ (1) $xyz = constant$ (2) $xy + yz + zx = constant$ (3) $(x^{2} + y^{2}) (y^{2} + z^{2}) (z^{2} + x^{2}) = constant$ (4) $(x + y) (y + z) (z + x) = constant$ 120. $The potential is varying with distance (x) as V = \frac{1}{2} (y^{2} - 4 x) volt. The electric field at x = 1 m and y = 1 m is$ (1) $2 i + j Vm^{- 1}$ (2) $- 2 i + j V m^{- 1}$ (3) $2 i - j Vm^{- 1}$ (4) $- 2 i + 2 j Vm^{- 1}$