Title 10-advanced-problem-package-.pdf ✅

Electrostatics 1. S is a solid neutral conducting sphere. A point charge q = 1 × 10−6C is placed at point A. C is the centre of sphere and AB is a tangent BC = 3 m and AB = 4 m. (A) The electric potential at B due to induced charge on the sphere is 1.2kV. (B) The electric potential at B due to induced charge on the sphere is −1.2kV. (C) The electric potential at B due to induced charge on the sphere is −0.45kV. (D) The electric potential at B due to induced charge on the sphere is 0.45kV. 2. Consider a uniformly charged hemispherical shell shown below. Indicate the directions (not magnitude) of the electric field at the central point P1 and an off-centre point P2 on the drumhead of the shell. (A) (B) (C) (D) 3. On an imaginary planet the acceleration due to gravity is same as that on Earth but there is also a downward electric field that is uniform close to the planet's surface. A ball of mass m carrying a charge q is thrown upward at a speed v and hits the ground after an interval t. What is the magnitude of potential difference between the starting point and the top point of the trajectory? (A) mv 2q (v − gt 2 ) (B) mv q (v − gt 2 ) (C) mv 2q (v − gt) (D) 2mv q (v − gt) 4. A system consists of a uniformly charged sphere of radius R and a surrounding medium filled by a charge with the volume density ρ = α/r, where α is a positive constant and r is the distance from the centre of the sphere. Find the charge of the sphere for which the electric field intensity E outside the sphere is independent of r. (A) α/2 ∈ 0 (B) 2/α ∈ 0 (C) 2παR 2 (D) None of these
5. Between two infinitely long wires having linear charge densities λ and −λ there are two points A and B as shown in the figure. The amount of work done by the electric field in moving a point charge q0 from A to B is equal to : (A) λq0 2πε0 ln 2 (B) − 2λq0 πε0 ln 2 (C) 2λq0 πε0 ln 2 (D) λq0 πε0 ln 2 6. Figure shows two conducting thin concentric shells of radii r and 3r. The outer shell carries charge q and inner shell is neutral. The amount of charge which flows from inner shell to the earth after the key K is closed, is equal to: (A) −q/3 (B) q/3 (C) 3q (D) − 3q 7. A uniformly charged rod is kept on y-axis with centre at origin, as shown. Which of the following actions will increase the electric field strength at the position of the dot which lies at right bisector of rod. (A) make the rod longer without changing the charge (B) make the rod shorter without changing the charge (C) make the rod shorter without changing the linear charge density (D) rotate the rod about yy' 8. A circular disk of radius ' a ' has uniform surface charge density σ on one side. The potential at a point P on the circumference is: (A) σa πε0 (B) 2σa πε0 (C) σa 2πε0 (D) 4σa πε0 9. Four point charges, +q, +q and −q, −q are placed on the vertices of a regular tetrahedron of edge length a. Each vertex has one point charge. The magnitude of equivalent dipole moment of the tetrahedron is: (A) Zero (B) qa√2 (C) 2qa (D) Not Defined 10. Positive charge Q is distributed uniformly over a circular ring of radius R. A particle having a mass m and a negative charge −q, is placed on its axis at distance X(x ≪ R) from the centre. The particle is now released from rest. Then the time period of oscillation of the particle will be. (Neglect gravity) (A) [ 4π 3ε0mR 3 Qq ] 1/2 (B) [ 8π 3ε0mR 3 Qq ] 1/2 (C) [ 32π 3ε0mR 3 Qq ] 1/2 (D) [ 16π 3ε0mR 3 Qq ] 1/2 11. Three concentric metallic spherical shells of radii R, 2R, 3R, are given the charges Q1,Q2,Q3 respectively. It is found that the surface charge densities on the outer surface of the shells are equal. Then, the ratio of the charges given to the shells,
Q1:Q2:Q3 is : (A) 1: 2: 3 (B) 1: 3: 5 (C) 1: 4: 9 (D) 1: 8: 18 12. A conducting shell having inner radius R1 and outer radius R2 contains a charge +q which is placed at a distance x from its centre. Field at an exterior point P which is situated at a distance r from centre of shell (r > R2 ) (A) Depends on x (B) Depends on R1 and R2 (C) Depends only on r (D) None of these 13. A solid conducting sphere of radius 2R, carrying charge Q is surrounded by two point charges Q and 2Q as shown in the figure. The electric field at point P due to the induced charges on conducting sphere is : (A) 7 16 KQ R2 towards right (B) 1 8 KQ R2 towards right (C) KQ R2 towards right (D) Zero 14. Two small electric dipoles of dipole moment pjˆ and −piˆ are situated at (0,0,0) and (r, 0,0) respectively. The electric potential at a point ( r 2 , √3r 2 , 0) is : (A) p(√3+1) 8π∈0r 2 (B) 0 (C) p 2πε0r 2 (D) p 8πε0r 2 15. The centres of two identical small spheres are 1 m apart. They carry charges of opposite kind and attract each other with a force f. When they are connected by a conducting wire of negligible capacitance they repel each other with a force f/3. Find the ratio of charges carried by the spheres initially. (A) 4: 1 (B) 3: 1 (C) 2: 1 (D) 1: 1 MULTIPLE CORRECT ANSWERS TYPEEach of the following Question has 4 choices A, B, C & D, out of which ONE or MORE Choices may be Correct: 16. A particle of mass m and charge q is thrown in a region where uniform gravitational field and electric field are present. The path of particle (Neglect relativistic effects) (A) may be a straight line (B) may be a circle (C) may be a parabola (D) may be a hyperbola 17. For the situation shown in the figure, mark out the correct statement(s) (A) Potential of the conductor is q 4πε0(d+R) (B) Potential of the conductor is q 4πε0d Hollow neutral conductor (C) Potential of the conductor can't be determined as nature of distribution of induced charges is not known (D) Potential at point B due to induced charges is −qR 4πε0(d+R)d 18. A spherical conductor of radius 2R has a spherical cavity of radius R 2 . The cavity does not enclose the centre of sphere. Charges Q1 and Q2 are placed as shown in figure. Q2 is at the center of cavity. An additional charge Q3 is given to the sphere.
(A) The potential of the sphere is KQ1 3R + K(Q2+Q3 ) 2R (B) The potential inside the cavity at a distance r (r < R 2 ) from the center of cavity is { kQ1 3R − 2kQ2 R + kQ2 r + kQ3 2R + kQ2 2R } (C) The value of potential outside the sphere at a distance r from the center of sphere is k(Q2+Q3 ) r + kQ1 r ′ where r ' is the distance from Q1 (D) The charge that will flow into ground if the sphere is grounded Q2 + Q3 + 2Q1 3 19. Two large conducting plates having surface charge densities +σ and −σ, respectively, are fixed ' d ' distance apart. A small test charge q of mass m is attached to two identical springs as shown in the adjacent figure. The charge q is now released from rest with springs in natural length. Then q will [neglect gravity] (A) perform SHM with angular frequency √ 2k m (B) perform SHM with amplitude σq 2kε0 (C) not perform SHM, but will have a periodic motion (D) remain stationary 20. Imagine a dipole is at the centre of an imaginary spherical surface. If magnitude of electric field at a certain point on the surface of sphere is 10 N/C, then which of the following cannot be the magnitude of electric field anywhere on the surface of sphere (A) 4 N/C (B) 8 N/C (C) 16 N/C (D) 32 N/C 21. When positively charged sphere is brought near a metallic sphere, it is observed that a force of attraction exists between two. It means: (A) metallic sphere is necessarily negatively charged. (B) metallic sphere may be electrically neutral (C) metallic sphere may be negatively charged (D) nothing can be said about charge of metallic sphere. 22. Which of the following aspects is correct, when an uncharged metal sphere is placed in a uniform electric field & electrostatic condition has been achieved (A) The metal sphere will become charged now. (B) The induced charges appearing on the surface of the sphere produce an electric field, at each point within the sphere & outside sphere. (C) The electric field lines, just outside the sphere are normal to the spherical surface. (D) The electric field lines in the spherical region decrease, as soon as the sphere is placed. 23. Three equal point charges (Q) are kept at the three corners of an equilateral triangle ABC of side a. P is a point having equal distance a from A, B and C. If E is the magnitude of electric field and V is the potential at point P, then (A) E = 3Q 4πε0a2 (B) E = √6Q 4πε0a2 (C) V = 3Q 4πε0a (D) E = 3√6Q 4πε0a2 24. Figure shows three spherical shells in separate situations, with each shell having the same uniform positive net charge. Points 1,4 and 7 are at the same radial distances from the centre of the their respective shells; so are points 2,5 and 8 ; and so are points 3,6 and 9. With the electric potential taken equals to zero at an infinite distance, choose correct statement. (A) Point 3 has highest potential (B) Point 1, 4 and 7 are at same potential