Electrostatics PYQs Set 4 (PDF)

Set 4 of 13 · Questions 91-120 of 385

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Mere Teacher · Previous Year Questions JEE Main Physics · Electrostatics · Set 4 (Q91-120)
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91. $If two charges q_{1} and q_{2} are separated with distance 'd' and placed in a medium of dielectric constant K. What will be the equivalent distance between charges in air for the same electrostatic force?$ (1) $d K$ (2) $k d$ (3) $1.5 d k$ (4) $2 d k$ 92. $A simple pendulum has a bob with mass m and charge q . The pendulum string has negligible mass. When a uniform and horizontal electric field E is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium position is____. (g: acceleration due to gravity)$ (1) $m^{2} g^{2} + q^{2} E^{2}$ (2) $mg + qE$ (3) $mg - qE$ (4) $m^{2} g^{2} - q^{2} E^{2}$ 93. $If potential (in volts) in a region is expressed as V (x, y, z) = 6 xy - y + 2 yz, the electric field (in N/C) at point (1, 1, 0) is$ (1) $- (3 i + 5 j + 3 k)$ (2) $- (6 i + 5 j + 2 k)$ (3) $- (2 i + 3 j + k)$ (4) $- (6 i + 9 j + k)$ 94. $Identify the WRONG statement in the case of electric field lines.$ (1) $They do not pass through an insulator.$ (2) $They do not pass through a conductor.$ (3) $They start from a positive charge and end on a negative charge.$ (4) $They do not intersect each other.$ 95. $An electron in potentiometer wire experiences a force 2.4 \times 10^{- 19} N . The length of potentiometer wire is 6 m . The e.m.f. of the battery connected across the wire is (electronic charge = 1.6 \times 10^{- 19} C)$ (1) $6 V$ (2) $9 V$ (3) $12 V$ (4) $15 V$ 96. $If the electric potential at a point on the surface of a hollow conducting sphere of radius R is V, then the electric potential at a point which is at distance \frac{R}{3} from the center of the sphere is$ (1) $V$ (2) $\frac{V}{3}$ (3) $\frac{V}{9}$ (4) $3 V$ 97. $Which statement(s) among the following are incorrect? (i) A negative test charge experiences a force opposite to the direction of the field. (ii) The tangent drawn to a line of force represents the direction of electric field. (iii) The electric field lines never intersect. (iv) The electric field lines form a closed loop.$ (1) $Only (i)$ (2) $Both (ii) and (iii)$ (3) $Only (iii)$ (4) $Only (iv)$ 98. $A copper rod AB of length l is rotated about end A with a constant angular velocity ω. The electric field at a distance x from the axis of rotation is$ (1) $\frac{m ω ^{2} x}{e}$ (2) $\frac{mωx}{el}$ (3) $\frac{mx}{ω ^{2} l}$ (4) $\frac{me}{ω ^{2} x}$ 99. $A parallel plate capacitor has a uniform electric field E in the space between the plates. If the distance between the plates is d and area of each plate is A, the energy stored in the capacitor is$ (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) $ϵ_{0} EAd$ 100. $The electrostatic potential inside a charged sphere is given as V = A r^{2} + B, where r is the distance from the center of the sphere, A and B are constants. Then, the charge density in the sphere is$ (1) $16 A ϵ_{0}$ (2) $- 6 A ϵ_{0}$ (3) $20 A ϵ_{0}$ (4) $- 15 A ϵ_{0}$ 101. $Two point charges - 4 μc and 4 μc, constituting an electric dipole, are placed at (- 9, 0, 0) cm and (9, 0, 0) cm in a uniform electric field of strength 10^{4} NC^{- 1} . The work done on the dipole in rotating it from the equilibrium through 180^{\circ} is:$ (1) $18.4 mJ$ (2) $14.4 mJ$ (3) $12.4 mJ$ (4) $16.4 mJ$ 102. $Electric field at a distance r from an infinitely long uniformly charged straight conductor, having linear charge density λ is E_{1} . Another uniformly charged conductor having same linear charge density λ is bent into a semicircle of radius r. The electric field at its center is E_{2} . Then$ (1) $E_{2} = πr E_{1}$ (2) $E_{2} = \frac{E _{1}}{r}$ (3) $E_{1} = E_{2}$ (4) $E_{1} = πr E_{2}$ 103. $If \oint E \cdot dS = 0 over a surface, then [NEET 2023]$ (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) $the number of flux lines entering the surface must be equal to the number of flux lines leaving it.$ 104. $If E_{a} and E_{q} represent the electric field intensity due to a short dipole at a point on its axial line and on the equatorial line at the same distance ' r ' from the centre of the dipole, then$ (1) $E_{a} = E_{q}$ (2) $E_{a} = \frac{1}{2} E_{q}$ (3) $E_{a} = \frac{1}{2} E_{q}$ (4) $E_{a} = 2 E_{q}$ 105. $The electrostatic potential due to an electric dipole at a distance ' r ' varies as:$ (1) $r$ (2) $\frac{1}{r ^{2}}$ (3) $\frac{1}{r ^{3}}$ (4) $\frac{1}{r}$ 106. $A List I A. Gauss’s Law in Electrostatics B. Faraday’s Law C. Gauss’s Law in Magnetism D. Ampere Maxwell Law Lost II I. \oint E \cdot d l = - \frac{d φ _{B}}{dt} II. \oint B . d A = 0 III. \oint B . d l = μ_{0} i_{C} + μ_{0} \in_{0} \frac{d φ _{E}}{dt} IV. \oint E . d s = \frac{q}{ϵ _{0}} Choose the correct answer from the options given below:$ (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) $A-II, B-III, C-IV, D-I$ 107. $A simple pendulum with a bob of mass 40 g and charge + 2 μC makes 20 oscillation in 44 s . A vertical electric field magnitude 4.2 \times 10^{4} NC^{- 1} pointing downward is applied. The time taken by the pendulum to make 15 oscillation in the electric field is (acceleration due to gravity = 10 ms^{- 2})$ (1) $30 s$ (2) $60 s$ (3) $90 s$ (4) $15 s$ 108. $In a region, the potential is represented by V (x, y, z) = 6 x - 8 xy - 8 y + 6 yz, where V is in volts and x, y, z are in metres. The electric force experienced by a charge of 2 coulomb situated at point (1, 1, 1) is$ (1) $65 N$ (2) $30 N$ (3) $24 N$ (4) $435 N$ 109. $A point dipole p = - p_{0} x kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively: (Take V = 0 at infinity)$ (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) $\frac{( p )}{4 π ϵ _{0} d ^{2}}, \frac{- p}{4 π ϵ _{0} d ^{3}}$ 110. $Two point charges + 8 μC and + 12 μC repel each other with a force of 48 N . When an additional charge of - 10 μC is given to each of these charges (the distance between the charges is unaltered) then the new force is$ (1) $repulsive force of 24 N$ (2) $attractive force of 24 N$ (3) $repulsive force of 12 N$ (4) $attractive force of 2 N$ 111. $A point charge +q is placed at the centre of a cube of side l. The electric flux emerging from the cube is$ (1) $\frac{6 q l ^{2}}{ϵ _{0}}$ (2) $\frac{q}{6 l ^{2_{8_{0}}}}$ (3) $zero$ (4) $\frac{q}{ϵ _{0}} .$ 112. $Ratio of thermal energy released in two resistor R and 3R connected in parallel in an electric circuit is:$ (1) $3 : 1$ (2) $1 : 1$ (3) $1 : 3$ (4) $1 : 27$ 113. $The electric potential at a point in free space due to charge Q coulomb is Q \times 1 0^{11} volts. The electric field at that point is$ (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) $12 π ϵ_{0} Q \times 1 0^{20} volt / m$ 114. $Two equal and opposite charges of masses m_{1} and m_{2} are accelerated in an uniform electric field through the same distance. What is the ratio of their accelerations if their ratio of masses is \frac{m _{1}}{m _{2}} = 0.5 ?$ (1) $\frac{a _{1}}{a _{2}} = 2$ (2) $\frac{a _{1}}{a _{2}} = 0.5$ (3) $\frac{a _{1}}{a _{2}} = 3$ (4) $\frac{a _{1}}{a _{2}} = 1$ 115. $The electric potential at a point (x, y, z) is given by V = - x^{2} y - x z^{3} + 4 . The electric field at that point is$ (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) $E = i (2 xy + z^{3}) + j x^{2} + k 3 x z^{2}$ 116. $In a certain region of space with volume 0.2 m^{3}, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is [NEET 2020]$ (1) $0.5 N / C$ (2) $1 N / C$ (3) $5 N / C$ (4) $zero$ 117. $An electric dipole is kept in non-uniform electric field. It generally experiences$ (1) $A torque but not a force$ (2) $A force and torque$ (3) $Neither a force nor a torque$ (4) $A force but not a torque.$ 118. $Three small identical bubbles of water having same charge on each coalesce to form a bigger bubble. Then the ratio of the potentials on one initial bubble and that on the resultant bigger bubble is :$ (1) $3^{2/3} : 1$ (2) $1 : 2^{2/3}$ (3) $1 : 3^{2/3}$ (4) $1 : 3^{1/3}$ 119. $An electric charge 10^{- 6} μC is placed at origin (0, 0) m of X - Y co-ordinate system. Two points P and Q are situated at (3, 3) m and (6, 0) m respectively. The potential difference between the points P and Q will be:$ (1) $3 V$ (2) $6 V$ (3) $0 V$ (4) $3 V$ 120. $The electric field in a region is given by E = (2 i + 4 j + 6 k) \times 10^{3} N / C . The flux of the field through a rectangular surface parallel to x - z plane is 6.0 Nm^{2} C^{- 1} . The area of the surface is _________cm^{2} .$