Electrostatics PYQs Set 12 (PDF)

Set 12 of 13 · Questions 331-360 of 385

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Mere Teacher · Previous Year Questions JEE Main Physics · Electrostatics · Set 12 (Q331-360)
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331. $The electric field in a certain region is acting radially outward and is given by E = Ar . A charge contained in a sphere of radius a centred at the origin of the field will be given by$ (1) $4 π ϵ_{0} A a^{2}$ (2) $A ϵ_{0} a^{2}$ (3) $4 π ϵ_{0} A a^{3}$ (4) $ϵ_{0} A a^{3}$ 332. $The electric field in a certain region is acting radially outward and is given by E = Ar. A charge contained in a sphere of radius 'a' centered at the origin of the field, will given by:$ (1) $A \in_{0} a^{2}$ (2) $4 π \in_{0} A a^{3}$ (3) $\in_{0} A a^{3}$ (4) $4 π \in_{0} A a^{2}$ 333. $In the figure, a very large plane sheet of positive charge is shown. P_{1} and P_{2} are two points at distance L and 2L from the charge distribution. If σ is the surface charge density, then the magnitude of electric fields E_{1} and E_{2} at P_{1} and P_{2} respectively are:$ (1) $E_{1} = σ / ϵ_{0}, E_{2} = σ /2 ϵ_{0}$ (2) $E_{1} = 2 σ / ϵ_{0}, E_{2} = σ / ϵ_{0}$ (3) $E_{1} = E_{2} = σ /2 ϵ_{0}$ (4) $E_{1} = E_{2} = σ / ϵ_{0}$ 334. $Two identical conducting spheres P and S with charge Q on each, repel each other with a force 16 N . A third identical uncharged conducting sphere R is successively brought in contact with the two spheres. The new force of repulsion between P and S is:$ (1) $1 N$ (2) $6 N$ (3) $12 N$ (4) $4 N$ 335. $In the figure, the value of q so that the electrostatic potential energy of the system becomes zero is$ (1) $\frac{q}{2}$ (2) $\frac{- 2 q}{2 + 2}$ (3) $\frac{2 q}{2 - 2}$ (4) $2 q$ 336. $Two particles A and B having charges 20 μC and - 5 μC respectively are held fixed with a separation of 5cm. At what position a third charged particle should be placed so that it does not experience a net electric force? \frac{20 μC}{A} 5 cm - 5 μC$ (1) $At 5cm from 20 μC on the left side of system$ (2) $At 5cm from - 5 μC on the right side$ (3) $At 1.25cm from - 5 μC between two charges$ (4) $At midpoint between two charges$ 337. $Two capacitors of 3 μF and 6 μF are connected in series and a potential difference of 900 V is applied across the combination. They are then disconnected and reconnected in parallel. The potential difference across the combination is$ (1) $zero$ (2) $100 V$ (3) $200 V$ (4) $400 V$ 338. $Two-point charges 2 q and q are placed at vertex A and centre of face CDEF of the cube as shown in figure. The electric flux passing through the cube is:$ (1) $\frac{3 q}{2 ϵ _{0}}$ (2) $\frac{3 q}{4 ϵ _{0}}$ (3) $\frac{q}{ϵ _{0}}$ (4) $\frac{3 q}{ϵ _{0}}$ 339. $Two point charges A and B, having charges +Q and -Q respectively, are placed at certain distance apart and force acting between them is F. If 25 % charge of A is transferred to B, then force between the charges becomes [NEET 2019]$ (1) $\frac{9 F}{16}$ (2) $\frac{16 F}{9}$ (3) $\frac{4 F}{3}$ (4) $F$ 340. $A charge Q is distributed over two concentric conducting thin spherical shells radii r and R (R > r) . If the surface charge densities on the two shells are equal, the electric potential at the common center is$ (1) $\frac{1}{4 π ϵ _{0}} \frac{( R + r )}{( R ^{2} + r ^{2} )} Q$ (2) $\frac{1}{4 π ϵ _{0}} \frac{( R + 2 r ) Q}{2 ( R ^{2} + r ^{2} )}$ (3) $\frac{1}{4 π ϵ _{0}} \frac{( R + r )}{2 ( R ^{2} + r ^{2} )} Q$ (4) $\frac{1}{4 π ϵ _{0}} \frac{( 2 R + r )}{( R ^{2} + r ^{2} )} Q$ 341. $Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in figure:$ (1) $3 ql \frac{j - i}{2}$ (2) $\frac{i - j}{2}$ (3) $2 ql j$ (4) $- 3 ql j$ 342. $The electric field (E) in (N C^{- 1}) in a region is given by E = 3 i^+ 5 j^. The net electric flux through a square area of side 2 m parallel to y - z plane is$ (1) $3 NC^{- 1} m^{2}$ (2) $6 NC^{- 1} m^{2}$ (3) $12 NC^{- 1} m^{2}$ (4) $24 NC^{- 1} m^{2}$ 343. $A conducting sphere of radius 0.1 m has uniform charge density 1.8 μC / m^{2} on its surface. The electric feld in free space at radial distance 0.2 m from a point on the surface is (ϵ_{0} =) permittivity of free space)$ (1) $\frac{6 \times 1 0 ^{- 6}}{ϵ _{0}} V m^{- 1}$ (2) $\frac{6 \times 1 0 ^{- 8}}{ϵ _{0}} V m^{- 1}$ (3) $\frac{2 \times 1 0 ^{- 7}}{ϵ _{0}} V m^{- 1}$ (4) $\frac{1 \times 1 0 ^{- 7}}{ϵ _{0}} V m^{- 1}$ 344. $An electron of mass m, charge e falls through a distance h meter in a uniform electric field E. Then time of fall$ (1) $t = \frac{2 hm}{e E}$ (2) $t = \frac{2 hm}{e E}$ (3) $t = \frac{2 e E}{hm}$ (4) $t = \frac{2 eE}{hm}$ 345. $Two charged conducting spheres of radii a and b are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:$ (1) $\frac{a}{b}$ (2) $ab$ (3) $\frac{b}{a}$ (4) $ab$ 346. $Match List - I with List - II Choose the correct answer from the options given below: List-I (A) Electric field inside (distance r > 0 from center of a uniformly charged spherical shell with surface charge density σ, and radius R. (B) Electric field at distance r>0 from a uniformly charged infinite plane sheet with surface charge density σ . (C) Electric field outside (distance r>0 from center) of a uniformly charged spherical shell with surface charge density σ, and radius R. (D) Electric field between 2 oppositely charged infinite plane parallel sheets with uniform surface charge density σ . List-II (I) σ / ϵ_{0} (II) σ /2 ϵ_{0} (III) 0 (IV) \frac{σ R ^{2}}{ϵ _{0} r ^{2}}$ (1) $(A)-(III), (B)-(II), (C)-(IV), (D)-(I)$ (2) $(A)-(IV), (B)-(II), (C)-(III), (D)-(I)$ (3) $(A)-(II), (B)-(I), (C)-(IV), (D)-(III)$ (4) $(A)-(IV), (B)-(I), (C)-(III), (D)-(II)$ 347. $A dipole with two electric charges of 2 μC magnitude each, with separation distance 0.5 μm, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30^{\circ} from the axis, it tends to realign in the direction due to a torque. The value of torque is:$ (1) $2.5\times 1 0^{- 9} Nm$ (2) $2.5 \times 10^{- 12} Nm$ (3) $5 \times 10^{- 3} Nm$ (4) $5 \times 10^{- 9} Nm$ 348. $Identify the correct statements :(A) Electrostatic field lines form closed loops.(B) The electric field lines point radially outward when charge is greater than zero.(C) The Gauss - Law is valid only for inverse - square force.(D) The workdone in moving a charged particle in a static electric field around a closed path is zero.(E) The motion of a particle under Coulomb's force must take place in a plane. Choose the correct answer from the options given below:$ (1) $(A), (B), (D), (E) Only$ (2) $(A), (C), (E) Only$ (3) $(A), (B), (C), (D) Only$ (4) $(B), (C), (D), (E) Only$ 349. $A tiny spherical oil drop carrying a net charge q is balanced in still air, with a vertical uniform electric field of strength \frac{81}{7} π \times 10^{5} V / m . When the field is switched off, the drop is observed to fall with terminal velocity 2 \times 10^{- 3} m s^{- 1} . Here g = 9.8 m / s^{2} . Viscosity of air is 1.8 \times 10^{- 5} Ns / m^{2} and the density of oil is 900 kg m^{- 3} . The magnitude of ' q ' is$ (1) $1.6 \times 10^{- 19} C$ (2) $0.8\times 1 0^{- 19} C$ (3) $3.2 \times 10^{- 19} C$ (4) $8 \times 10^{- 19} C$ 350. $A dipole comprises of two charged particles of identical magnitude q and opposite in nature. The mass m of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance l. If the dipole is placed in a uniform electric field E; in such a way that dipole axis makes a very small angle with the electric field, E . The angular frequency of the oscillations of the dipole when released is given by:$ (1) $\frac{3 qE}{2 ml}$ (2) $\frac{8 qE}{ml}$ (3) $\frac{4 qE}{ml}$ (4) $\frac{8 qE}{3 ml}$ 351. $Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field. Reason (R): In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions. In the light of the above statements, choose the most appropriate answer from the options given below:$ (1) $Both (A) and (R) are correct and (R) is the correct explanation of (A).$ (2) $Both (A) and (R) are correct but (R) is not the correct explanation of (A)$ (3) $(A) is not correct but (R) is correct$ (4) $(A) is correct but (R) is not correct$ 352. $Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen. Reason R: Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. In the light of the above statements, choose the correct answer from the options given below.$ (1) $A is true but R is false$ (2) $Both A and R are true and R is the correct explanation of A$ (3) $Both A and R are true but R is NOT the correct explanation of A$ (4) $A is false but R is true$ 353. $There is an electric field E in x -direction. If the work done on moving a charge of 0.2 C through a distance of 2 m along a line making an angle 6 0^{o} with x -axis is 4 J, then what is the value of E ?$ (1) $5 N / C$ (2) $20 N / C$ (3) $3 N/C$ (4) $4 N / C .$ 354. $The electric field lines on the left have twice the separation on those on the right as shown in figure. If the magnitude of the field at A is 40 V m^{- 1}, what is the force on 20 μC charge kept at B ?$ (1) $16 \times 1 0^{- 4} N$ (2) $1 \times 1 0^{- 4} N$ (3) $4 \times 1 0^{- 4} N$ (4) $8 \times 1 0^{- 4} N$ 355. $Which of the statements is false in the case of polar molecules?$ (1) $Centers of positive and negative charges are separated in the absence of external electric field.$ (2) $Centers of positive and negative charges are separated in the presence of external electric field.$ (3) $Do not possess permanent dipole moments.$ (4) $Ionic molecule HCl is the example of polar molecule.$ 356. $The electric field at a distance \frac{3 R}{2} from the centre of a charged conducting spherical shell of radius R is E. The electric field at a distance \frac{R}{2} from the centre of the sphere is$ (1) $zero$ (2) $E$ (3) $\frac{E}{2}$ (4) $\frac{E}{3}$ 357. $Experimentally it is found that 12. 8 eV energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is \frac{9}{x} \times 1 0^{- 10} m . The value of the x is:_____. (1 eV - 1.6 x 10-19 J, \frac{1}{4 π ϵ _{0}} = 9 x 109 \frac{N m ^{2}}{C ^{2}} and electronic charge = 1.6 x 10-19 C)$ 358. $Two charges of - 4 μC and + 4 μC are placed at the points A (1, 0, 4) m and B (2, - 1, 5) m located in an electric field E = 0.20 iV / cm . The magnitude of the torque acting on the dipole is 8 α \times 10^{- 5} Nm, Where α =________$ 359. $At the centre of a half ring of radius R = 10 c m and linear charge density 4 n C m^{- 1}, the potential is x π V . The value of x is_____$ 360. $A positive ion A and a negative ion B has charges 6.67 \times 10^{- 19} C and 9.6 \times 10^{- 10} C, and masses 19.2 \times 10^{- 27} kg and 9 \times 10^{- 27} kg respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is P \times 10^{45}, where the value of 10 P is (Take \frac{1}{4 π ϵ _{0}} = 9 \times 10^{9} Nm^{2} C^{- 1} and universal gravitational constant as 6.67 \times 10^{- 11} Nm^{2} kg^{- 2}) Assume that charge may not be an integral multiple of electrons.$