Title 01. ELECTRIC CHARGES AND FIELDS.pdf ✅

#QID# 29796 (1.) A uniform electric field having a magnitude E0 and direction along the positive X − axis exists. If the potential V is zero as x = 0, then its value at X = +x will be (a.) V(x) = +x E0 (b.) Vx = −xE0 (c.) Vx = +x 2E0 (d.) Vx = −x 2E0 ANSWER: b EXPLANATION: (b) ∵ E = − dV dX ⇒ Vx = −xE0 #QID# 29797 (2.) Three condensers each of capacitance 2F are put in series. The resultant capacitance is (a.) 6F (b.) 3 2 F (c.) 2 3 F (d.) 5F ANSWER: c EXPLANATION: (c) 1 C = 1 2 + 1 2 + 1 2 ⇒ C = 2 3 F #QID# 29798 (3.) Two equally charged, identical metal spheres A and B repel each other with a force ′F ′ . The spheres are kept fixed with a distance ′r′
between them. A third identical, but uncharged sphere C is brought in contact with A and then placed at the mid-point of the line joining A and B. The magnitude of the net electric force on C is (a.) F (b.) 3F/4 (c.) F/2 (d.) F/4 ANSWER: a EXPLANATION: (a) Initially F = k Q2 r 2 ...(i) Finally Force on C due to A, FA = k(Q/2) 2 (r/2)2 = kQ2 r 2 Force on C due to B, FB = KQ(Q/2) (r/2)2 = 2kQ2 r 2 ∴ Net force on C, Fnet = FB − FA = kQ2 r 2 #QID# 29799 (4.) The law, governing the force between electric charges is known as (a.) Ampere’s law (b.) Ohm’s law (c.) Faraday’s law (d.) Coulomb’s law ANSWER: d #QID# 29800
(5.) If identical charges (−q) are placed at each corner of a cube of side b, then electric potential energy of charge (+q) which is placed at centre of the cub will be (a.) 8 √2q 2 4πε0b (b.) −8 √2q 2 πε0b (c.) −4 √2q 2 πε0b (d.) −4q 2 √3πε0b ANSWER: d EXPLANATION: (d) Length of the diagonal of a cube having each side b is √3b. So distance of centre of cube from each vertex is √3b 2 Hence potential energy of the given system of charge is U = 8 × [ 1 4πε0 . (−q)(q) √3b/2 ] = −4q 2 √3πε0b #QID# 29801 (6.) A body can be negatively charged by (a.) Giving excess of electrons to it (b.) Removing some electrons from it (c.) Giving some protons to it (d.) Removing some neutrons from it ANSWER: a #QID# 29802 (7.) Capacitance (in F) of a spherical conductor with radius 1m is (a.) 1.1 × 10−10 (b.) 10−6
(c.) 9 × 10−9 (d.) 10−3 ANSWER: a EXPLANATION: (a) C = 4π ∈0 R = 1 9 × 109 × 1 = 1.1 × 10−10F #QID# 29803 (8.) Total electric flux coming out of a unit positive charge put in air is (a.) ε0 (b.) ε0 −1 (c.) (4pε0 ) −1 (d.) 4πε0 ANSWER: b EXPLANATION: (b) Total flux coming out from unit charge φ = E⃗ . ds = 1 ε0 × 1 = ε0 −1 #QID# 29804 (9.) A capacitor is charged by using a battery which is then disconnected. A dielectric slab is then slipped between the plates, which results in (a.) Reduction of charge on the plates and increase of potential difference across the plates (b.) Increase in the potential difference across the plate, reduction in stored energy, but no change in the charge on the plates (c.) Decrease in the potential difference across the plates, reduction in the stored energy, but no change in the charge on the plates (d.) None of the above