Title 1A.ELECTROSTATICS(1-43).pdf ✅

NISHITH Multimedia India (Pvt.) Ltd., 1 ELECTROSTATICS NISHITH Multimedia India (Pvt.) Ltd., JEE - ADVANCED VOL - V ELECTROSTATICS LEVEL-V SINGLE ANSWER QUESTIONS CHARGE AND ITS PROPERTIES 1. The linear charge density of a thin metallic rod varies with the distance ‘x’ from one end as   2      0 x x l 0 .The total charge on the rod is A) 3 0 3  l B) 3 0 4  l C) 3 0 2 3  l D) 3 0 2  l 2. The linear charge density of a uniform semicircular wire varies with ' '  shown in the figure as 0     cos .If R is the radius of the loop, the charge on the wire is + + + + + + +++ + + + + + +  + R + + + + + +++ + + + + + +  R A) 0R B) 0 3 R C) 0 2 3  R D) 0 2 R 3. For the hemisphere of radius ‘R’ shown in the figure the surface charge density ' '  varies with ' '  (shown in figure) as 0     cos . The total charge on the sphere is + + + + + + +++ + + + + + +  + + + + + + +++ + + + + + +  A) 2 0 2 R B) 2 0 2   R C) 2 0 3   R D) 2  0 R COLOUMBS LAW & PRINCIPAL OF SUPERPOSITION 4. A charge ‘+Q’ is uniformily distributed along the circular arc of radius ‘R’ as shwon in figure. The magnitude of the force experienced by the point charge +q placed at the centre of cuvature is 0 1 4 k          + + + + + + + + + ++ R  R + + + + + + + + + ++ R  R A) 2 sin 2 kQq R   B) 2 2 sin 2 kQq R   C) 2 2 cos 2 kQq R   D) 2 2 tan 2 KQq R   5. A thin circular wire ring of radius ‘r’ has a charge ‘Q’. If a point charge ‘q’ is placed at the centre of ring then the tension in the wire will increase by A) 2 2 0 8 qQ   r B) 2 2 0 4 qQ   r C) 2 0 4 qQ  r        D) 2 2 0 2 qQ   r 6. Two metallic sphers each of mass M and radius R charged separately to Q1 and Q2 , are at a distance ‘d’ between their centres (d>2R). The force between them will be A) 1 2 2 0 1 4 Q Q   d B) 1 2 2 0 1 4 Q Q  d   C) 1 2 2 0 1 4 Q Q  d   D) zero
Jr Chemistry E/M ELECTROSTATICS 2 NISHITH Multimedia India (Pvt.) Ltd., JEE - ADVANCED VOL - V NISHITH Multimedia India (Pvt.) Ltd., 7. A positive point charge +Q is fixed in space. A negative point charge -q of mass m re- volves around fixed charge in elliptical or- bit. The fixed charge +Q is at one focus of the ellipse.The only force acting on nega- tive charge is the electrostatic force due to positive charge.Then which of the following statement is true. A) Linear momentum of negative point charge is conserved. B) Angular momentum of negative point charge about fixed positive charge is conserved. C) Total kinetic energy of negative point charge is conserved. D) Electrostatic potential energy of system of both point charges is conserved. 8. Find the force experienced by the semicircular rod charged with a charge q, placed as shown in figure. Radius of the wire is R and the line of charge with linear charge density l is passing through its centre and perpendicular to the plane of wire. (A) 2 R q 0 2    (B) R q 0 2    (C) 4 R q 0 2    (D) 4 R q 0   ELECTRIC FIELD AND LINES OF FORCE 9. Two identical point charges are placed at a separation of l. P is a point on the line joining the charges, at a distance x from any one charge. The field at P is E. E is plotted against x for values of x from close to zero to slightly less than l. Which of the following best represents the resulting curve? (A) (B) (C) (D) 10. Two infinitely large charged planes having uniform surface charge density +  and –  are placed along x-y plane and yz plane respectively as shown in the figure. Then the nature of electric lines of forces in x-z plane is given by : z – + X (A) Z X (B) Z X (C) Z X (D) Z X
NISHITH Multimedia India (Pvt.) Ltd., 3 ELECTROSTATICS NISHITH Multimedia India (Pvt.) Ltd., JEE - ADVANCED VOL - V ELECTRIC POTENTIAL & POTENTIAL ENERGY 11. A conducting bubble of radius “a” and thickness t t a    has a potential ‘V’. Now the bubble collapses into a droplet (of radius R). The electric potential on the droplet is A) 1 2 3 a V t       B) 1 2 3 3 a V t       C) 1 3 3 a V t       D)V 12. In the following diagram a uniform electric field of magnitude 325NC-1 is directed along ve y-direction. The co-ordinates of point A are (-20, -30) cm and those of point B are (40, 50)cm. The potential difference along the path shown is E x y C B A E x y C B A A) 260V B) 260V C) 130V D) 130V 13. An infinite long plate has surface charge density  , As shown in the fig. a point charge q is moved from A to B. Net work done by electric field is : (A)  0 q 2 (X1 – X2 ) (B)  0 q 2 (X2 – X1 ) (C)  0 q (X2 – X1 ) (D)  0 q ( 2 r r   ) 14. A conducting disc of radius R rotates about its axis with an angular velocity  . Then the potential difference between the centre of the disc and its edge is (no magnetic field is present) : (A) zero (B)  2 2 m R e 2e (C)  3 m R e 3e (D)  2 em R e 2 15. A neutral conducting spherical shell is kept near a charge q as shown. The potential at point P due to the induced charges is q r r' C P (A) kq r (B) kq r ' (C) kq kq – r r' (D) kq CP 16. The following diagram represents a semi circular wire of linear charge density 0     sin where 0 is a positive constant. The electric potential at ‘o’ is 0 1 4 take k          A) 0 k  sin B) 0 cos 2 k  C) zero D) 0 k  cos 17. The electric potential at the centre of hemisphere of radius ‘R’ having uniform surface charge density  is A) 0  R  B) 0 2 R  C) 0 2  R  D) 0 3  R  18. For an infinite line of charge having linear charge density ' '  lying along x-axis, the work done in moving a charge ‘q’ from C to A along CA is
Jr Chemistry E/M ELECTROSTATICS 4 NISHITH Multimedia India (Pvt.) Ltd., JEE - ADVANCED VOL - V NISHITH Multimedia India (Pvt.) Ltd., C B a A a + ++ + + ++ + + ++ + C B a A a + ++ + + ++ + + ++ + A) 0 ln 2 2 q   B) 0 ln 2 4 q   C) 0 ln 2 4 q   D)   0 ln 0.5 2 q   19. The diagram shows three infinitely long uniform line charges placed on the X, Y and Z axis. The work done in moving a unit positive charge from (1, 1, 1) to (0, 1, 1) is equal to (A) (l ln 2) / 2 e 0 (B) (l ln 2) / e 0 (C) (3l ln 2) / 2 e 0 (D) None 20. Two positively charged particles X and Y are initially far away from each other and at rest. X begins to move towards Y with some initial velocity. The total momentum and energy of the system are p and E. (A) If Y is fixed, both p and E are conserved. (B) If Y is fixed, E is conserved, but not p. (C) If both are free to move, p is conserved but not E. (D) If both are free, E is conserved, but not p. 21. A metal ball of radius R is placed concentrically inside a hollow metal sphere of inner radius 2R and outer radius 3R. The ball is given a charge +2Q and the hollow sphere a total charge – Q. The electrostatic potential energy of this system is : (A) 24 R 7Q 0 2  (B) 16 R 5Q 0 2  (C) 8 R 5Q 0 2  (D) None RELATION BETWEEN E & V 22. Figure shows an electric line of force which curves along a circular arc. The magnitude of electric field intensity is same at all points on this curve and is equal to E. If the potential at A is V, then the potential at B is A E B R  (A) V – ER (B) V – E2R sin  2 (C) V + ER (D) V + 2ER sin  2 23. Uniform electric field of magnitude 100 V/m in space is directed along the line y = 3 + x. Find the potential difference between point A (3, 1) & B (1, 3) (A) 100 V (B) 200 2 V (C) 200 V (D) 0 24. Electrical potential 'v' in space as a function of co-ordinates is given by, v = 1 x + 1 y + 1 z . Then the electric field intensity at (1, 1, 1) is given by : (A) – (i j k) ˆ ˆ ˆ   (B) ˆ ˆ ˆ i j k   (C) zero (D)   1 ˆ ˆ ˆ (i j k) 3 25. A graph of the x component of the electric field as a function of x in a region of space is shown. The Y and Z components of the