Gauss's Law PYQs Set 1 (PDF)

Set 1 of 4 · Questions 1-30 of 113

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Mere Teacher · Previous Year Questions JEE Main Physics · Gauss's Law · Set 1 (Q1-30)
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1. $Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densities on them? [NEET 2019]$ (1) $σ_{1} = \frac{5}{6}, σ, σ_{2} = \frac{5}{2} σ$ (2) $σ_{1} = \frac{5}{2} σ, σ_{2} = \frac{5}{6} σ$ (3) $σ_{1} = \frac{5}{2} σ, σ_{2} = \frac{5}{3} σ$ (4) $σ_{1} = \frac{5}{3} σ, σ_{2} = \frac{5}{6} σ$ 2. $Eight drops of mercury, each of same radius and same charge combine to form a bigger drop. The ratio of capacitance of the bigger drop to that of each smaller drop is$ (1) $8 : 1$ (2) $4 : 1$ (3) $2 : 1$ (4) $1 : 1$ 3. $Among the following the charge that does not exist on any type of charged body is$ (1) $3.2 \times 10^{- 19} C$ (2) $6.4 \times 10^{- 19} C$ (3) $9.6 \times 10^{- 20} C$ (4) $9.6 \times 10^{- 18} C$ 4. $Two metal spheres, one of radius R and the other of radius 2R respectively have the same surface charge density σ. They are brought in contact and separated. What will be the new surface charge densities on them?$ (1) $σ_{1} = \frac{5}{6} σ, σ_{2} = \frac{5}{2} σ$ (2) $σ_{1} = \frac{5}{2} σ, σ_{2} = \frac{5}{6} σ$ (3) $σ_{1} = \frac{5}{2} σ, σ_{2} = \frac{5}{3} σ$ (4) $σ_{1} = \frac{5}{3} σ, σ_{2} = \frac{5}{6} σ$ 5. $Suppose the charge of a proton and an electron differ slightly. One of them is - e, the other is (e + De). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then De is of the order of [Given mass of hydrogen m_{h} = 1.67 \times 1 0^{-27} kg$ (1) $1 0^{-20} C$ (2) $1 0^{-23} C$ (3) $1 0^{-37} C$ (4) $1 0^{-47} C$ 6. $The angle between the electric lines of force and the equipotential surface is [NEET 2022]$ (1) $45^{\circ}$ (2) $90^{\circ}$ (3) $180^{\circ}$ (4) $0^{\circ}$ 7. $If there is only one type of charge in the universe, then (E \to Electric field, d s \to Area vector)$ (1) $\oint E \cdot d s \neq = 0 on any surface$ (2) $\oint E \cdot d s could not be defined$ (3) $\oint E \cdot d s = \infty if charge is inside$ (4) $\oint E\cdotds=0 if charge is outside, = \frac{q}{ϵ _{0}} if charge is inside$ 8. $Two hollow conducting spheres of radii R_{1} and R_{2} (R_{1} > R_{2}) have equal charges. The potential would be [NEET 2022]$ (1) $more on smaller sphere$ (2) $equal on both the spheres$ (3) $dependent on the material property of the sphere$ (4) $more on bigger sphere$ 9. $Three charges +Q, q, +Q are placed respectively, at distance, 0, d/2 and d from the origin, on the x-axis. If the net force experienced by +Q, placed at x = 0, is zero, then value of q is:$ (1) $+Q/2$ (2) $+Q/4$ (3) $-Q/2$ (4) $-Q/4$ 10. $A gaussian sphere encloses an electric dipole within it. The total flux across the sphere is$ (1) $zero$ (2) $half that due to a single charge$ (3) $double that due to a single charge$ (4) $dependent on the position of the dipole.$ 11. $An electrostatic paint sprayer has a metal sphere of diameter 18 cm and at a potential of 25 kV . The charge on the metal sphere is$ (1) $0.25 μC$ (2) $2.5 μC$ (3) $0.5 μC$ (4) $25 μC$ 12. $Suppose the charge of a proton and an electron differ slightly. One of them is -e and the other is (e + Δ e). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much greater than atomic size) apart is zero, then Δ e is of the order [Given mass of hydrogen, m_{h} = 1.67 \times 10^{- 27} kg] [NEET 2017]$ (1) $10^{- 20} C$ (2) $10^{- 23} C$ (3) $10^{- 37} C$ (4) $10^{- 47} C$ 13. $A hollow spherical shell of radius r has a uniform charge density σ. It is kept in a cube of edge 3r such that the centers of the cube and the shell coincide. Then the electric flux coming out of one face of a cube is (ϵ_{0} - permittivity of free space)$ (1) $\frac{π r ^{2} σ}{ϵ _{0}}$ (2) $\frac{5 ϵ _{0}}{2 π r ^{2} σ}$ (3) $\frac{π r ^{2} \cdot σ}{6 ϵ _{0}}$ (4) $\frac{2 π r ^{2} σ}{3 ϵ _{0}}$ 14. $Charge q_{2} is at the centre of a circular path with radius r . Work done in carrying charge q_{1}, once around this equipotential path, would be$ (1) $\frac{1}{4 π ε _{0}} \times \frac{q _{1} q _{2}}{r ^{2}}$ (2) $\frac{1}{4 π ε _{0}} \times \frac{q _{1} q _{2}}{r}$ (3) $zero$ (4) $infinite.$ 15. $Find out the surface charge density at the intersection of point x = 3 m plane and x -axis, in the region of uniform line charge of 8 nC / m lying along the z -axis in free space.$ (1) $0.424 nCm^{- 2}$ (2) $47.88 C / m$ (3) $0.07 nCm^{- 2}$ (4) $4.0 nCm^{- 2}$ 16. $A charge Q is enclosed by a Gaussian spherical surface of radius R. If the radius is doubled, then the outward electric flux will$ (1) $increase four times$ (2) $be reduced to half$ (3) $remain the same$ (4) $be doubled$ 17. $An electron is released from a distance of 4 m from a stationary point charge 20 nC . What will be the speed of the electron when it is 2 m away from the point charge? [Charge of electron = 1.6 \times 10^{- 19} C, mass of electron = 9 \times 10^{- 31} kg, \frac{1}{4 π ϵ} = 9 \times 10^{9} S.I unit]$ (1) $2 \times 10^{6} m / s$ (2) $4 \times 10^{6} m / s$ (3) $1.6 \times 10^{6} m / s$ (4) $2.4 \times 10^{6} m / s$ 18. $A charge q is placed at the centre of the line joining two exactly equal positive charges Q . The system of three charges will be in equilibrium, if q is equal to$ (1) $- Q$ (2) $Q /2$ (3) $- Q /4$ (4) $+ Q$ 19. $The potential of a large liquid drop when eight liquid drops are combined is 20 V . Then the potential of each single drop was$ (1) $10 V$ (2) $7.5 V$ (3) $5 V$ (4) $2.5 V$ 20. $When an α-particle of mass 'm' moving with velocity ' v ' bombards on a heavy nucleus of charge 'Ze' its distance of closet approach from the nucleus depends on m as:$ (1) $m$ (2) $\frac{1}{m}$ (3) $\frac{1}{m}$ (4) $\frac{1}{m ^{2}}$ 21. $The expression for electric field intensity at a point outside uniformly charged thin plane sheet is (d is the distance of point from plane sheet)$ (1) $independent of d.$ (2) $directly proportional to d .$ (3) $directly proportional to d.$ (4) $directly proportional to \frac{1}{d} .$ 22. $Two metallic spheres of radii 1 cm and 2 cm are given charges 1 0^{- 2} C and 5 \times 1 0^{- 2} C respectively. If they are connected by a conducting wire, the final charge on the smaller sphere is$ (1) $3 \times 1 0^{- 2} C$ (2) $4 \times 1 0^{- 2} C$ (3) $1 \times 1 0^{- 2} C$ (4) $2 \times 1 0^{- 2} C$ 23. $In finding the electric field using gauss law the formula \| E \to \| = \frac{q _{inc}}{ϵ _{o} \| A \|} is applicable. In the formula ϵ_{o} is permittivity of free space, A is the area of Gaussian surface and q_{inc} is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?$ (1) $Surface is equipotential$ (2) $Magnitude of electric field is constant$ (3) $Magnitude of electric field is constant and the surface is equipotential$ (4) $For all Gaussian surfaces.$ 24. $If a charge on the body is 1 nC, then how many electrons are present on the body?$ (1) $6.25 \times 10^{27}$ (2) $1.6 \times 10^{19}$ (3) $6.25 \times 10^{28}$ (4) $6.25 \times 10^{9}$ 25. $Two charged spherical conductors of radii R_{1} and R_{2} are connected by a wire. Then, the ratio of surface charge densities of the spheres (σ_{1} / σ_{2}) is [NEET 2021]$ (1) $\frac{R _{1}}{R _{2}}$ (2) $\frac{R _{2}}{R _{1}}$ (3) $(\frac{R _{1}}{R _{2}})$ (4) $\frac{R _{1}^{2}}{R _{2}^{2}}$ 26. $A mass of 1 kg carrying a charge of 2 C is accelerated through a potential of 1 V . The velocity acquired by it is$ (1) $2 m s^{- 1}$ (2) $2 m s^{- 1}$ (3) $\frac{1}{2} ms s^{- 1}$ (4) $\frac{1}{2} m s^{- 1}$ 27. $In air, a charged soap bubble of radius r is in equilibrium having outside and inside pressures being equal. The charge on the drop is (ϵ_{0} = permittivity of free space, T = surface tension of soap solution)$ (1) $4 π r^{2} \frac{2 T ϵ _{0}}{r}$ (2) $4 π r^{2} \frac{4 T ϵ _{0}}{r}$ (3) $4 π r^{2} \frac{6 T ϵ _{0}}{r}$ (4) $4 π r^{2} \frac{8 T ϵ _{0}}{r}$ 28. $Assertion (A): In a region of constant potential, the electric field is zero and there can be no charge inside the region. Reason (R): According to Gauss law, charge inside the region should be zero if electric field is zero.$ (1) $Both (A) and (R) are true; (R) is correct explanation of (A)$ (2) $Both (A) and (R) are true; (R) is not correct explanation of (A)$ (3) $(A) is true, (R) is false$ (4) $(A) is false, (R) is true$ 29. $512 identical drops of mercury are charged to a potential of 2 V each. The drops are joined to form a single drop. The potential of this drop is _____ V.$ 30. $The total charge enclosed in an incremental volume 2 \times 1 0^{- 9} m^{3} of located at the origin is ____ nC, if electric flux density of its field is found as D = e^{- x} sin y i - e^{- x} cos y j + 2 z k C / m^{2} .$