Tiêu đề 1-electrostatics-.pdf ✅

Electrostatics 1. A simple pendulum of length l has a bob of mass m, with a charge q on it A vertical sheet of charge, with surface charge density σ passes through the points of suspension. At equilibrium, the string makes an angle θ with the vertical, then : (A) tan θ = σq 2ε0mg (B) tan θ = σq ε0mg (C) cot θ = σq 2ε0mg (D) cot θ = σq ε0mg 2. A charged particle of mass m and charge q is released from rest in an electric field of constant magnitude E. the kinetic energy of the particle after time t will be : (A) 2E 2 t 2 mq (B) Eq 2m 2t 2 (C) E 2q 2 t 2 2m (D) Eqm 2t 3. A charge Q is distributed over two concentric hollow spheres of radius r and R(> r) such that the surface densities are equal. The potential at the common centre is: (A) Q(R 2+r 2 ) 4πε0(R+r) (B) Q R+r (C) Zero (D) Q(R+r) 4πε0 (R2+r 2) 4. If ∮ S E ̅ ⋅ dS̅̅̅̅ = 0 over a surface, then : (A) The electric field inside the surface and on it is zero (B) The electric field inside the surface is necessarily uniform (C) The number of flux lines entering the surface must be equal to the number of flux lines leaving it (D) Net charge, if any, must necessarily be outside the surface 5. The ratio of the forces between two small spheres with same charges when they are in air to when they are in a medium of dielectric constant K is : (A) 1:K (B) K: 1 (C) 1:K 2 (D) K 2 : 1 6. Two point charges 2q and 8q are placed at a distance r apart. Where should a third charge −q be placed between them so that the electrical potential energy of the system is a minimum : (A) At a distance of r/3 from 2q (B) At a distance of 2r/3 from 2q (C) At a distance of r/16 from 2q (D) None of these 7. A spherical conductor A of radius r placed concentrically inside a conducting shell B of radius R(R > r). A charge Q is given to A, and then A is joined to B by a metal wire. The charge flowing from A and B will be : (A) Q ( R R+r ) (B) Q ( r R+r ) (C) Q (D) Zero 8. A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at distance L from the end A is : (A) Q 8πε0L (B) 3Q 4πε0L (C) Q 4πε0Lln 2 (D) Qln 2 4πε0L 9. If a conductor has a potential V ≠ 0 and there are no charges anywhere else outside, then : (A) There must be charges on the surface or inside itself (B) There cannot be any charge in the body of the conductor (C) There must be charges only on the surface (D) There must be charges inside the surface 10. A non-conducting ring of radius R has charge Q distributed uniformly over it. If rotates with an

(D) All of these 18. An electric dipole of common P⃗ is placed at the origin along the x-axis. The electric field at a point P, whole position vector makes an angle θ with the x- axis, will make an angle : (A) α (B) θ (C) θ + α (D) 2θ + α with the x-axis, where tan α = 1 2 tan θ 19. A charge q is placed at a distance a/2 above the centre of a horizontal square surface of edge a as shown in figure. The electric flux through the square surface is : (A) Q/2ε0 (B) Q/ε0 (C) Q/6ε0 (D) Q/8ε0 20. A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at the centre of the shell. The electrostatic potential at a point P at a distance R/2 from the centre of the shell is : (A) 2Q 4πε0R (B) 2Q 4πε0R − 2q 4πε0R (C) 2Q 4πε0R + q 4πε0R (D) (q+Q) 4πε0 2 R 21. The work done to move a charge along an equipotential from A to B : (A) cannot be defined as −∫A B E. dl (B) must be defined as −∫A B E. dl (C) is zero (D) can have a non-zero value 22. In figure shown, conducting shells A and B have charges Q and 2Q distributed uniformly over A and B. The value of VA − VB is : (A) Q 4πε0R (B) Q 8πε0R (C) 3Q 4πε0R (D) 3Q 8πε0R 23. The region between two concentric spheres of radii ' a ' and ' b ', respectively (see figure), has volume charge density ρ = A r where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is :
(A) Q 2πa2 (B) Q 2π(b2−a2) (C) 2Q π(a2−b2) (D) 2Q πa2 24. A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is: (A) Zero everywhere (B) Non-zero and uniform (C) Non-uniform (D) Zero only at its centre 25. Within a spherical charge distribution of charge density ρ(r), N equipotential surfaces of potential V0,V0 + ΔV, V0 + 2ΔV, ... ... . V0 + NΔV(ΔV > 0), are drawn and have increasing radii r0, r1, r2, ... . rN, respectively. If the difference in the radii of the surfaces is constant for all values of V0 and ΔV then : (A) ρ(r) = constant (B) ρ(r) ∝ 1 r 2 (C) ρ(r) ∝ 1 r (D) ρ(r) ∝ r 26. If there were only one type of charge in the universe, then : (A) ∮ S E. dS ≠ 0 on any surface (B) ∮ S E. dS = 0 if the charge is outside the surface (C) ∮ S E. dS could not be defined (D) ∮ S E. dS = q ε0 if charges of magnitude q were inside the surface 27. A long cylindrical shell carries positive surface charge σ in the upper half and negative surface charge −σ in the lower half. The electric field lines around the cylinder will look like figure given in : (Figures are schematics and not drawn to scale) (A) (B) (C) (D)