Electrostatics PYQs Set 13 (PDF)

Set 13 of 13 · Questions 361-385 of 385

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Mere Teacher · Previous Year Questions JEE Main Physics · Electrostatics · Set 13 (Q361-385)
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361. $Energy per unit volume for a capacitor having area A and separation d kept at potential difference V is given by$ (1) $\frac{1}{2} ϵ_{0} \frac{V ^{2}}{d ^{2}}$ (2) $\frac{1}{2 ϵ _{0}} \frac{V ^{2}}{d ^{2}}$ (3) $\frac{1}{2} C V^{2}$ (4) $\frac{Q ^{2}}{2 C}$ 362. $When air is replaced by a dielectric medium of constant K, the maximum force of attraction between two charges separated by a distance$ (1) $increases K times$ (2) $remains unchanged$ (3) $decreases K times$ (4) $increases K^{- 1} times.$ 363. $Charges -q and +q located at A and B, respectively constitute an electric dipole. Distance AB = 2 a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP = y and y >> 2 a . The charge Q experiences and electrostatic force F. If Q is now moved along the equatorial line to P ’ such that O P^{’} = (\frac{y}{3}) the force on Q will be close to: (\frac{y}{3} >> 2 a)$ (1) $3F$ (2) $F/3$ (3) $9F$ (4) $27F$ 364. $Configuration (a) Configuration (b)$ (1) $\frac{K q _{0}^{2}}{a} (4 - 22)$ (2) $\frac{K q _{0}^{2}}{a} (3 - 2)$ (3) $\frac{Kq _{0}^{2}}{a} (42 - 2)$ (4) $\frac{Kq _{0}^{2}}{a} (32 - 2)$ 365. $Electric charge is transferred to an irregular metallic disk as shown in the figure. If σ_{1}, σ_{2}, σ_{3} and σ_{4} are charge densities at given points then, choose the correct answer from the options given below: (A) σ_{1} > σ_{3}; σ_{2} = σ_{4} (B) σ_{1} > σ_{2}; σ_{3} > σ_{4} (C) σ_{1} > σ_{3} > σ_{2} = σ_{4} (D) σ_{1} < σ_{3} < σ_{2} = σ_{4} (E) σ_{1} = σ_{2} = σ_{3} = σ_{4}$ (1) $B and C Only$ (2) $A and C Only$ (3) $D and E Only$ (4) $A, B and C Only$ 366. $The electric field at a distance \frac{3 R}{2} from the center of a charged conducting spherical shell of radius R is E. The electric field at a distance \frac{R}{2} from the centre of the sphere is$ (1) $zero$ (2) $E$ (3) $\frac{E}{2}$ (4) $\frac{E}{3}$ 367. $An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity 10^{6} m / s . If the magnitude of the electric field between the plates is 9.1 V / cm, then the vertical component of velocity of electron is (mass of electron = 9.1 \times 10^{- 31} kg and charge of electron = 1.6 \times 10^{- 19} C)$ (1) $0$ (2) $1 \times 10^{6} m / s$ (3) $16 \times 10^{6} m / s$ (4) $16 \times 10^{4} m / s$ 368. $A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E . Due to the force q E, its velocity increases from 0 to 6 m s^{- 1} in one second duration. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between 0 to 3 seconds are respectively$ (1) $2 m s^{- 1}, 4 m s^{- 1}$ (2) $1 m s^{- 1}, 3 m s^{- 1}$ (3) $1 m s^{- 1}, 3.5 m s^{- 1}$ (4) $1.5 m s^{- 1}, 3 m s^{- 1}$ 369. $A small bob of mass 100 mg and charge + 10 μC is connected to an insulating string of length 1 m. It is brought near to an infinitely long nonconducting sheet of charge density ' σ ' as shown in figure. If string subtends an angle of 45^{\circ} with the sheet at equilibrium the charge density of sheet will be. (Given, ϵ_{0} = 8.85 \times 10^{- 12} \frac{F}{m} and acceleration due to gravity, g = 10 \frac{m}{s ^{2}})$ (1) $1.77 nC / m^{2}$ (2) $0.885 nC / m^{2}$ (3) $885 nC / m^{2}$ (4) $17.7 nC / m^{2}$ 370. $Two small spherical balls of mass 10 g each with charges - 2 μC and 2 μC, are attached to two ends of very light rigid rod of length 20 cm. The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of 100 μC / m^{2} such that length of rod makes an angle of 30^{\circ} with electric field generated by charge sheet. Net torque acting on the rod is: (Take ϵ_{o} : 8.85 \times 10^{- 12} C^{2} / Nm^{2})$ (1) $1.12 Nm$ (2) $2.24 Nm$ (3) $11.2 Nm$ (4) $112 Nm$ 371. $If the electric potential at any point (x, y, z)m in space is given by V = 3 x^{2} volt. The electric field at the point (1, 0, 3) m will be:$ (1) $3 V m^{- 1}, directed along positive x-axis.$ (2) $3 V m^{- 1}, directed along negative x-axis.$ (3) $6 V m^{- 1}, directed along positive x-axis.$ (4) $6 V m^{- 1}, directed along negative x-axis$ 372. $Three charged particles A, B and C with charges -4q, 2q and -2q are present on the circumference of a circle of radius d. The charged particles A, C and center O of the circle formed an equilateral triangle as shown in figure. Electric field at O along x-direction is$ (1) $\frac{3 q}{π ε _{0} d ^{2}}$ (2) $\frac{3 q}{4 π ε _{0} d ^{2}}$ (3) $\frac{3 3 q}{4 π ε _{0} d ^{2}}$ (4) $\frac{2 3 q}{π ε _{0} d ^{2}}$ 373. $A charge q is placed at the center of one of the surface of a cube. The flux linked with the cube is:$ (1) $\frac{q}{2 ϵ _{0}}$ (2) $\frac{q}{8 ϵ _{0}}$ (3) $Zero$ (4) $\frac{q}{4 ϵ _{0}}$ 374. $Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure:$ (1) $- 3 q l j$ (2) $(q l) \frac{i + j}{2}$ (3) $2ql j$ (4) $3 q l \frac{j - i}{2}$ 375. $As shown in the figure, a point charge Q is placed at the center of conducting spherical shell of inner radius a and outer radius b. The electric field due to charge Q in three different regions I, II and III is given by : (I: r < a, II: a < r < b, III: r > b)$ (1) $E_{I} = 0, E_{I I} = 0, E_{I I I} \neq = 0$ (2) $E_{I} \neq = 0, E_{I I} = 0, E_{I I I} \neq = 0$ (3) $E_{I} \neq = 0, E_{I I} = 0, E_{I I I} = 0$ (4) $E_{I} = 0, E_{I I} = 0, E_{I I I} = 0$ 376. $A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)$ (1) (2) (3) (4) 377. $Given below are two statements: Statement - I: An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero but the electric field is not zero anywhere in the sphere. Statement - II: If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r(<R) is zero but the electric flux passing through this closed spherical surface of radius r is not zero. In the light of the above statements. Choose the correct answer from the option given below:$ (1) $Statement I is true but Statement II is false.$ (2) $Statement I is false but Statement II is true.$ (3) $Both Statement I and Statement II are true.$ (4) $Both Statement I and Statement II are false.$ 378. $Considering a group of positive charges, which of the following statements is correct?$ (1) $Net potential of the system cannot be zero at a point but net electric field can be zero at that point.$ (2) $Net potential of the system at a point can be zero but net electric field can't be zero at that point.$ (3) $Both the net potential and the net field can be zero at a point.$ (4) $Both the net potential and the net electric field cannot be zero at a point.$ 379. $Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R) with radial distance (r) from the center?$ (1) (2) (3) (4) 380. $The given graph shown variation (with distance r from center) of:$ (1) $Electric field of a uniformly charged sphere$ (2) $Potential of a uniformly charged spherical shell$ (3) $Potential of a uniformly charged sphere$ (4) $Electric field of a uniformly charged spherical shell$ 381. $Electric field at center O of semicircle of radius a having linear charge density λ given as$ (1) $\frac{2 λ}{ϵ _{0} a}$ (2) $\frac{λπ}{ϵ _{0} a}$ (3) $\frac{λ}{2 π ϵ _{0} a}$ (4) $\frac{λ}{π ϵ _{0} a}$ 382. $Two charged thin infinite plane sheets of uniform surface charge density σ_{+} and σ_{-} where \| σ_{+} \| > \| σ_{-} \| intersect at right angle. Which of the following best represents the electric field lines for this system?$ (1) (2) (3) (4) 383. $A thin infinite sheet charge and an infinite line charge of respective charge densities + σ and + λ are placed parallel at 5 m distance from each other. Points P and Q are at \frac{3}{π} m and \frac{4}{π} m perpendicular distances from line charge towards sheet charge, respectively. E_{p} and E_{q} are the magnitudes of resultant electric field intensities at point P and Q respectively. If \frac{E _{P}}{E _{Q}} = \frac{4}{a} for 2 (σ) = \|A\|, then the value of a is_____.$ 384. $An infinite plane sheet of charge having uniform surface charge density + σ_{s} C / m^{2} is placed on x - y plane. Another infinitely long line charge having uniform linear charge density + λ_{e} C / m is placed at z = 4 m plane and parallel to y -axis. If the magnitude values (σ_{s}) = 2 (λ_{e}) then at point (0, 0, 2), the ratio of magnitudes of electric field values due to sheet charge to that of line charge is π n : 1 . The value of n is _____$ 385. $A thin metallic wire having cross sectional area of 10^{- 4} m^{2} is used to make a ring of radius 30 cm . A positive charge of 2 πC is uniformly distributed over the ring, while another positive charge of 30 pC is kept at the centre of the ring. The tension in the ring is______ N; provided that the ring does not get deformed (neglect the influence of gravity). (given, \frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} SI units)$