Electrostatics PYQs Set 1 (PDF)

Set 1 of 13 · Questions 1-30 of 385

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Mere Teacher · Previous Year Questions JEE Main Physics · Electrostatics · Set 1 (Q1-30)
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1. $An electric dipole of moment p is lying along a uniform electric field E . The work done in rotating the dipole by 9 0^{o} is$ (1) $pE$ (2) $2 pE$ (3) $pE /2$ (4) $2pE.$ 2. $Consider two charged metallic spheres S_{1} and S_{2} of radii R_{1} and R_{2}, respectively. The electric fields E_{1} (on S_{1}) and E_{2} (on S_{2}) on their surfaces are such that E_{1} / E_{2} = R_{1} / R_{2} . Then the ratio V_{1} (on S_{1})/ V_{2} (on S_{2}) of the electrostatic potentials on each sphere is$ (1) $(\frac{R _{1}}{R _{2}})^{3}$ (2) $\frac{R _{1}}{R _{2}}$ (3) $(\frac{R _{2}}{R _{1}})$ (4) $(\frac{R _{1}}{R _{2}})^{2}$ 3. $A parallel plate capacitor of capacitance C_{1} with a dielectric slab in between its plates is connected to a battery. It has a potential difference V_{1} across its plates. When the dielectric slab is removed, keeping the capacitor connected to the battery, the new capacitance and potential difference are C_{2} and V_{2} respectively. Then,$ (1) $V_{1} = V_{2}, C_{1} < C_{2}$ (2) $V_{1} > V_{2}, C_{1} > C_{2}$ (3) $V_{1} < V_{2}, C_{1} > C_{2}$ (4) $V_{1} = V_{2}, C_{1} > C_{2}$ 4. $What is the electric potential at a distance of 9 cm from 3 nC ?$ (1) $300 V$ (2) $270 V$ (3) $30 V$ (4) $3 V$ 5. $A parallel plate air capacitor has capacity C, distance of separation between plates is D and potential difference V is applied between the plates. Force of attraction between the plates of the parallel plate air capacitor is$ (1) $\frac{C V ^{2}}{d}$ (2) $\frac{C ^{2} V ^{2}}{2 d ^{2}}$ (3) $\frac{C ^{2} V ^{2}}{2 d}$ (4) $\frac{C V ^{2}}{2 d}$ 6. $Identical charges (-q) are placed at each corners of cube of side b then electrostatic potential energy of charge (+q) which is placed at centre of cube will be$ (1) $\frac{- 4 2 q ^{2}}{π ϵ _{0} b}$ (2) $\frac{- 8 2 q ^{2}}{π ϵ _{0} b}$ (3) $\frac{- 4 q ^{2}}{3 π ϵ _{0} b}$ (4) $\frac{8 2 q ^{2}}{4 π ϵ _{0} b}$ 7. $Two positive point charges of 10 μC and 12 μC are placed 10 cm apart in air. The work done to bring them 6 cm closer is$ (1) $8.1 J$ (2) $3.2 J$ (3) $9 J$ (4) $None$ 8. $A positive charge particle of 100 mg is thrown in opposite direction to a uniform electric field of strength 1 x 1 0^{5} N C^{- 1} . If the charge on the particle is 40µC and the initial velocity is 200 m s^{- 1}, how much distance it will travel before coming to the rest momentarily:$ (1) $1m$ (2) $5 m$ (3) $10 m$ (4) $0.5 m$ 9. $The radius of a soap bubble is r and the surface tension of the soap solution is S. The electric potential to which the soap bubble be raised by charging it so that the pressure inside the bubble becomes equal to the pressure outside the bubble is (ϵ_{0} =) permittivity of the free space$ (1) $\frac{Sr}{8 ϵ _{0}}$ (2) $\frac{Sr}{4 ϵ _{0}}$ (3) $\frac{4 Sr}{ϵ _{0}}$ (4) $\frac{8 Sr}{ϵ _{0}}$ 10. $The net electric flux due to a uniform electric field of 3 \times 10^{3} 1 NC^{- 1} through a cube of side 20 cm oriented such that its faces are parallel to the coordinate planes is$ (1) $30 Nm^{2} C^{- 1}$ (2) $15 Nm^{2} C^{- 1}$ (3) $0$ (4) $20 Nm^{2} C^{- 1}$ 11. $Pick out the statement which is incorrect.$ (1) $The electric field lines forms closed loop.$ (2) $Field lines never intersect.$ (3) $The tangent drawn to a line of force represents the direction of electric field.$ (4) $A negative test charge experiences a force opposite to the direction of the field.$ 12. $The electric potential V at any point (x, y, z), all in meters in space is given by V = 4 x^{2} volt. The electric field at the point (1, 0, 2) in volt/meter is:$ (1) $8 along positive X-axis$ (2) $16 along negative X-axis$ (3) $16 along positive X-axis$ (4) $8 along negative X-axis$ 13. $An infinitely long thin straight wire has uniform charge density of \frac{1}{4} \times 10^{- 2} Cm^{- 1} . What is the magnitude of electric field at a distance 20 cm from the axis of the wire?$ (1) $2.25 \times 10^{8} N C^{- 1}$ (2) $9 \times 10^{8} N C^{- 1}$ (3) $1.12 \times 10^{8} N C^{- 1}$ (4) $4.5 \times 10^{8} NC^{- 1}$ 14. $A spherical conductor of radius 2 cm is uniformly charged with 3 nC . What is the electric field at a distance of 3 cm from the centre of the sphere?$ (1) $3 \times 10^{4} V m^{- 1}$ (2) $3 \times 10^{6} V m^{- 1}$ (3) $3 \times 10^{- 4} V m^{- 1}$ (4) $3 V m^{- 1}$ 15. $A vertical electric field of magnitude 4.9 x 1 0^{5} N/C just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be: (Given g = 9.8 m/ s^{2})$ (1) $1. 6 x 1 0^{- 9} C$ (2) $2. 0 x 1 0^{- 9} C$ (3) $3.2 x 1 0^{- 9} C$ (4) $0.5 x 1 0^{9} C$ 16. $A particle of mass m and charge q travelling with a velocity v along the x-axis enters a uniform electric field E directed along the y-axis. What will be the trajectory of the particle?$ (1) $Circular$ (2) $Elliptical$ (3) $Parabolic$ (4) $Helical$ 17. $Inside a charged hollow sphere, at any point the electric field (E) and potential (V) are$ (1) $V = 0 and E = 0$ (2) $V is constant and E = 0$ (3) $V = 0 and E is constant$ (4) $V is constant and E is constant$ 18. $In the uniform electric field of E = 1 \times 10^{4} NC^{- 1}, an electron is accelerated from rest. The velocity of the electron when it has travelled a distance of 2 \times 10^{- 2} m is nearly ... m s m^{- 1} (e / m) of electron (= 1.8 \times 10^{11} Ckg^{- 1})$ (1) $1.6 \times 10^{6}$ (2) $0.85 \times 10^{6}$ (3) $0.425 \times 10^{6}$ (4) $8.5 \times 10^{6}$ 19. $If ϵ_{0} denotes the permittivity of free space and Φ_{E} is the flux of the electric field through the area bounded by the closed surface, then dimensions of (ϵ_{0} \frac{d φ _{E}}{dt}) are that of:$ (1) $electric charge$ (2) $electric field$ (3) $electric current$ (4) $electric potential$ 20. $The acceleration of an electron due to the mutual attraction between the electron and a proton when they are 1.6Å apart is, (m_{e} = 9 \times 10^{- 31} kg, e = 1.6 \times 10^{- 19} C) (Take, , \frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} Nm^{2} C^{- 2}) [NEET 2020]$ (1) $10^{24} m / s^{2}$ (2) $10^{23} m / s^{2}$ (3) $10^{22} m / s^{2}$ (4) $10^{25} m / s^{2}$ 21. $Two metal spheres of radius R and 3R have same surface charge density σ. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes σ_{1} and 2, respectively. The ratio \frac{σ _{1}}{σ _{2}} is$ (1) $\frac{1}{3}$ (2) $\frac{1}{9}$ (3) $9$ (4) $3$ 22. $A spherical volume contains a uniformly distributed charge of density 1.0 \times 10^{- 6} C / m^{3} . Find the electrical field (in N / C) at a point inside the volume at a distance 1 mm from the centre. (Let (\frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} Nm^{2} C^{- 2})$ (1) $\frac{8}{π}$ (2) $6π$ (3) $\frac{π}{6}$ (4) $12 π$ 23. $The electric potential at a place is varying as V = \frac{1}{2} (y^{2} - 4 x) volt. Then the electric field at x = 1 m and y = 1 m is$ (1) $2 i + j V m^{- 1}$ (2) $- 2 i + j V m^{- 1}$ (3) $2 i - j V m^{- 1}$ (4) $- 2 i + 2 j Vm^{- 1}$ 24. $A block of mass ' m ' and charge ' q ' is connected to a point ' O ' with an inextensible string. This system is on a horizontal table. An electric field (E) is applied perpendicular to the string and in the plane of the horizontal table. The tension in the string when it becomes parallel to the electric field is$ (1) $qE$ (2) $2 qE$ (3) $\frac{3 q E}{4}$ (4) $3 qE$ 25. $A plane electromagnetic wave of frequency 100 MHz is travelling in vacuum along the x- direction. At a particular point in space and time, B = 2.0 \times 10^{- 8} k T where, k is unit vector along Z -direction) What is E at this point?$ (1) $0.6 j V / m$ (2) $6.0 k V / m$ (3) $6.0 j V / m$ (4) $0.6 k V / m$ 26. $A system of two charges separated by a certain distance apart stores electrical potential energy. If the distance between them is increased, the potential energy of the system,$ (1) $may increase or decrease$ (2) $increases in any case$ (3) $remains the same$ (4) $decreases in any case.$ 27. $A point charge causes an electric flux of - 2 \times 10^{4} Nm^{2} C^{- 1} to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is : (Given ϵ_{0} = 8.85 \times 10^{- 12} C^{2} N^{- 1} m^{- 2})$ (1) $15.7 \times 10^{- 8} C$ (2) $17.7 \times 10^{- 8} C$ (3) $-15.7\times 1 0^{- 8} C$ (4) $-17.7\times 1 0^{- 8} C$ 28. $A conducting sphere of radius R is given a charge Q. The electric potential and the electric field at the center of the sphere respectively are$ (1) $zero and \frac{Q}{4 π ϵ _{0} R ^{2}}$ (2) $\frac{Q}{4 π ϵ _{0} R} and zero$ (3) $\frac{Q}{4 π ϵ _{0} R} and \frac{Q}{4 π ϵ _{0} R ^{2}}$ (4) $both are zero$ 29. $The electric field in a region is given by E = (\frac{3}{5} E_{0} i + \frac{4}{5} E_{0} j) \frac{N}{c} . The ratio of flux of reported field through the rectangular surface of area 0.2 m² (parallel to y - z plane ) to that of the surface of area 0.3m² (parallel to x-z plane ) is a: b, a = where ____ (round off to nearest integer) [Here, i, j and k are unit vectors along x, y and z axes respectively]$ 30. $In an electrical circuit, a battery is connected to pass 20C of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at 15V. The work done by the battery is ________J.$