30 A point charge q is surrounded by eight identical charges at distance r as shown in figure How much work is done by the forces of electrostatic repulsion when the point charge at the centre is removed to infinity 1 Zero 8q 4Teor 9 q q 9 0 9 9 Eor d q 9 2 9 3 Electrostatics of Conductors Dielectrics and Polarization Capacitors and Capacitance 8q 4Teor 31 1000 small water drops each of capacitance C join together to form one large spherical drop The capacitance of bigger sphere is 1 C 2 10 C 3 100 C 4 1000 C 32 Two similar conducting balls having charges q and q are placed at a separation d from each other in air The radius of each ball is r and the separation between their centres is d d r Calculate the capacitance of the two ball system 64q 4Teor 1 4TE 2 2 3 4rloge 4 4rloge The Parallel Plate Capacitor Effect of Dielectrics on Capacitance Combination of Capacitors 33 Two parallel plate capacitors have their plate areas 100 cm and 500 cm respectively If they have the same charge and potential and the distance between the plates of the first capacitor is 0 5 mm then the distance between the plates of the second capacitor is 1 0 10 cm 2 0 15 cm 00 34 A dielectric slab of dielectric constant K is placed between the plates of a parallel plate capacitor carrying charge q The induced charge q on the surface of slab is given by q 1 q q 2 q q K 4 d a 1 1 0 05 36 3 q q 35 Two charged capacitors have their outer plates fixed and inner plates connected by a spring of force constant K The charge on each capacitor is q Find the extension in the spring at equilibrium mhm 1 2AEok q A ok ka edice IIT JEEF 3 5 A d 3 4 Zero The following arrangement consists of five identical metal plates parallel to each other Area of each plate is A and separation between the successive plates is d The capacitance between P and Q is 4 EA 3 d q K 1 K fig A 1 2d 3 2 3d 2 3 3d 4 k www smooth q 2 4A ok 2 A Q 37 A capacitor is half filled with a dielectric K 2 as shown in figure A If the same capacitor is to be filled with same dielectric as shown what would be the thickness of dielectric so that capacitor still has same capacity 5 EA d fig B d