Electrostat-04-OBJECTIVE UNSOLVED LEVEL - I

OBJECTIVE LEVEL - I A 1. Three uncharged capcitors of capacities C1, C2 and C3 are conencted to one an- other as shown in the figure. Points A, B and D are at potential V1, V2 and V3 . then the potential at O will be V1C1  V2C2  V3C3 V1  V2  V3 (a) C  C  C (b) C  C  C B D 1 2 3 V1 V2  V3  1 2 3 V1V2 V3 (c) C C  C  (d) C C C 1 2 3 1 2 3 2. A charge +Q is uniformly distributeed over a thin ring of radius R, velocity of an electron at the moment it passes through the centre O of the ring, if the electron was initially at rest at a point A which is very far away from the centre and on the axis of the ring is (a) (c) (b) (d) kQe mR . 3. A rod AB of mass m and length l is positively charged with linear charge density  coul/m. It is provided at end A and is hanging freely. If a horizontal electric field E is switched on in the region, find the angular acceleration of the rod with which it starts. (a) E 2m 3E (b) 3E 2m (c) m (d) zero . 4. 1000 small water drops each of radius r and charge q coalesce together to form one spherical drop. The potential of the big drop is larger than that of the smaller drops by a factor of : (a) 1000 (b) 100 (c) 10 (d) 1. 5. Two equally charged small balls placed at a fixed distance, experience a force F. A similar uncharged ball after touching one of them, is placed at the midpoint of the two balls. The force experienced by this ball is : (a) F/2 (b) F (c) 2F (d) 4F. 6. Two concentric spheres of radius R and 2R have charges Q and 2Q. The potential at a point P situated at a point 3R/2 distance from common centre is V, now outer sphere is earthed, the potential at point P now is : (a) V/5 (b) V/10 (c) V/3 (d) V. 7 From a supply of identical capacitors rated 8 mF, 250V, the minimum number of capacitors required to form a composite 16 mF, 1000V is : (a) 2 (b) 4 (c) 16 (d) 32. 8. Two capacitor C and 2C in parallel are charged with a battery of voltage V and then isolated. Now a dielectric of relative permittivity k is filled in C V (a) the final p.d. across the combination is (b) the final p.d. across the combination is 3k  1 3V k  2 2V (c) the final p.d. across the combination is k V (d) the final p.d. across the combination is 2k  1 . 9. A parallel plate capacitor has an electric field of 5 x 106 V/m between the plates, If the charge on the capacitor plate is 0.5 mC, then the force on each capacitor plate is : (a) 1.25 Nt (b) 2.5 Nt (c) 0.125 Nt (d) none of these . 10. An infinite number of charges each equal to q are placed along the x = 1, x = 2, x = 4, …………….. and so on the potential V and the electric field E at the points x = 0 due to this set of charges is : (a) V  q , E  1 4 q (b) V  2q , E  4 q 4πε 0 4πε 0 3 4πε 0 3 4πε 0 (c) V  2q , E  q (d) V  4 q , E  2q . 4πε 0 4πε 0 3 4πε 0 4πε 0 11. A parallel plate capacitor of area ‘A’ plate separation ‘d’ is filled with two dielectrics as shown. What is the capacitance of the arrangement ? A/2 A/2 (a) (c) 3K0A 4d k  10 A 2d (b) (d) 4K0A d 3d k k  30A 2k  1d . 12. In the arrangement shown the charging battery is disconnect and a directric slab of dielelctric constnat ‘K’ is inserted between the plate of capacitor C. V 2C What is the final potential difference across ‘2C’ ? (a) zero (b) V Q are shown. the charge on outer shell is Q. What charge should be given to inner sphere so that the potential at poitn ‘p’ outside the outer sphere is zero ? (a)  Qr R (b) (b)  QR r (c) – Q (d) d  2QR . r 14. Correct plot of d vs  in case of an electric dipole placed in any uniform electric field is (a) (b) (c) (d) . 15. A metal sphere A of radius a is charged to a potential V. What will be its potential if it is enclosed by a sphereical conductiing shell B of radius b and the two are connected by a wire av B b a A (a) b (b) V 40 Va (c) a  b (d) zero. OBJECTIVE LEVEL - II 1. A solid conducting sphere of radius a having a charge q is surrounded by a concentric conducting spherical shell of inner radius 2a and outer radius 3a as shown in figure. Find the amount of heat produced when switch is closed. (a) (c) Kq 2 2a Kq 2 4a (b) (d) Kq 2 3a Kq 2 6a . 2. Figure shows a ball having a charge q fixed at a point A. Two identical balls having charges +q and –q and mass ‘m’ each are attached to the ends of a light rod of length 2a. The rod is free to rotate about a fixed axis perpendicular to the plane of the papper and passing through the mid-point of the rod. The system is re- leased from the situation shown in figure. Find the angular velocity of the rod when the rod becomes horizontal. +q A 2a 2a (a) 2q 3π  ma 3 q (b) –q 0 q (c) (d) 4π  2q ma 3 . 0 3. Two hollow non conducting spheres of radius a are separated by a distance 2a and having charge +q and –q. If they are moved apart to a distance 4a and while moving their radii also expended to double the initial value. Work done by external force in doing so is : (a) kq2 a (b) kq 2  kq2 a  kq2 (c) 4a (d) 4a . 4. There are two concentric spherical conducting shells of radii r and 3r. The outer shell carries a charge q and inner is uncharged but connected to earth with a key which is open. Find the amount of charge flows from inner shell to earth when the key is closed. (a) -q/3 (b) q/3 (c) 3q (d) -3q . 5. A capacitor of capacitance C is charged by connecting it to a battery of e.m.f. E volts. The capacitor is now disconnected and reconnected to the same battery with polarity reversed. The heat energy developed in the connecting wire is : (a) CE2 (b) 2CE2 1 (c) 2 CE2 (d) zero . 6. There are three concentric shell having charges (+q, 0, +q) with outer is connected to earth, then (a) the inner surfaces of middle and outer shells will have the same charge (b) the inner surfaces of middle and outer shells will have same charge density (c) the outer surface of all the three shells will have the same charge (d) the outer surface of the three shells will have same charge density. 7. Two metal spheres of radii a and b are connected by a thin wire. Their separation is large compared with their dimensions. The capacitance of this system is (a) 4 0 ab (b) 2 0 (a+b) (c) 4 0 (a+b) (d) 2 0 (a2+b2). 8. In a parallel plate capacitor connected to a battery, the plates are pulled apart with a uniform speed. When the separation between the plates is d, the rate of change of the energy stored in the capacitor is proportional to (a) d2 (b) d (c) 1/d (d) 1/d2 . 9. A capacitor of capacitance C0 is charged to a potential V0 and them isolate. A small capacitor C is then charged from C0, discharged and charged again and the process is repeated n times. Due to this potential of the larger capacitor is decreased to V. Value of C is : V 1/ n  V 1 / n  (a) C0   (b) C0  0   V   1      V n  (c) C0  V   V0   1  (d) C0    V0   1 .  10. The equivalent capacitance between points A and B is A B (a) 3  F (b) 4  F (c) 6  F (d) 8  F. 11. Three capacitors of 1  F, 2  F and 3  F are initially a charged to 10  C, 20  C and 30  C respectively. Now these are connected as shown in figure. If switch is closed, final charge appearing on 1F , 2F and 3F capacitors, is s (a) 0 (b) 10  C each (c) 50/ 11  C, 160 /11  C and 390/11  C (d) 60/11  C, 40/11  C and 60/11  C. 12. The circular plates A and B of a parallel plate capacitor have a diameter of 0.1 m are 2x10-3 m apart. The plates C and D, of a similar capacitor have a diameter of 0.12 m and are 3x10-3m apart plate A is earthed, plates B and C are connected together, plate C is connected to appositive pole of a 120 V battery whose negative is earthed then the combined capacitance is :  49 πε  30 πε (a)  20  0 (b)  49  0      πε 0   6  (c)  2  (d)  5 πε0     13. A negatively charged rod is held near a conductor X that is earthed as shown in figure (a) Uncharged and at a negative potential – – (b) Uncharged and at a positive potential (c) Positively charged and at Earth potential (d) Negatively charged and at Earth potential 14. A, B, C, D, P and and Q are points in a uniform electric field. the potentials at these points are VA  2 Volt VP  VB  VD  5 Volt VC  8 Volt. the electric field at P is B C P A D 0.2 m (a) 10 V cm–1 along PQ (b) 15 V cm–1 along PA (c) 5 V cm–1 along PC (d) 5 V cm–1 along PA cm 15. Figure shows two equipotential lines X and Y. what is Ex and Ey Y (x and y conmponent of electric field) (a) +100 V/m, – 200 V/m (b) –100 V/m, + 200 V/m (c) + 200 V/m, +100 V/m (d) –200 V/m, – 100 V/m 2V O 2 4 6 8 cmX