Title 1. Electric Charge and Fields.pdf ✅

1. Electric charge is quantised. SI unit of charge is coulomb (C). The minimum unit of charge, which may reside independently is the electronic charge e having a value1.60 10 C. –19 × Charge on any other body is given by q ne = ± , where n is any integer. It is additive in nature. Charge is conserved, invariant and radiates energy. 2. Coulomb’s law states that if q q 1 2 and are two stationary point charges in free space separated by a distance r, then force of attraction/repulsion between them is given by F k q q r = 1 2 2 = ε ⋅ 1 4 0 1 2 2 π q q r In vector form, F r = ⋅ 1 4 0 1 2 3 πε q q r where, r r = r $ (vector form) ε0 = Permittivity of free space and k = = × 1 4 9 10 0 9 πε The value of ε0 in SI units is 8.854 C N m 2 –1 –2 × − 10 12 . 3. The force between two charges q1 and q2 located at a distance (r) in a medium is expressed as F q q r medium = ⋅ 1 4 1 2 2 πε (where, ε = absolute permittivity of the medium) F F q q r q q r vacuum medium = 4 ⋅ 1 4 1 0 1 2 2 1 2 2 πε πε = = = ε ε ε 0 r K (where, εr = relative permittivity of the medium) i.e., the ratio of permittivity of the medium to the permittivity of free space is called relative permittivity. 4. Superposition principle Resultant force on a point charge due to a number of point charges F F F F F 0 01 02 03 0 = + + + + K n 5. Electric field is the region surrounding an electric charge or a group of charges, in which another charge experiences a force. Its unit isN/C . It isa vector quantity. 6. Electric field vector E (also known as electric field intensity) at any point is given by E F = → lim q0 0 q0 where, q0 is a small positive test charge which experiences a force, F at given point. Electric field at a distance r from a point charge q is given by E q r = ε ⋅ 1 4 0 2 π 7. Electric field lines are a way of pictrorially mapping the electric field around a configuration of charge(s). These lines start on positive charge and end on negative charge. The tangent on these lines at any point gives direction of field at that point. 8. Electric flux is a measure of flow of electric field through a surface. Mathematically, electric flux is the product of an area element dS and normal component of E integrated over a surface, i.e., φ = E ∫ E dS cos θ = ⋅ = ⋅ ∫ ∫ E S E n d dS $ where n$ is the unit vector normal to area element dS. Electric Charge and Fields C H A P T E R 1 A Quick Recapitulation of the Chapter
Electric flux is a scalar having SI unit Nm C2 –1 or Vm. Its dimensional formula is [ML T A ]. 3 –3 –1 9. The arrangement of two equal and opposite point charges at a fixed distance is called an electric dipole. 10. The product of the magnitude of either charge ( ) q and the distance between the charges ( )2a is called electric dipole moment. p a = × q 2 It is a vector quantity and its SI unit is C-m. 11. Electric field at a point distant r from centre of dipole along its axial line is given by E p = ε ⋅ − 1 4 2 0 2 2 2 π r ( ) r a (direction of E is same as of p) 12. Electric field at a point distant r from centre of dipole along its equatorial line is given by E p = ε ⋅ + 1 4π 0 (r a 2 2 3/ 2 ) (direction of E is opposite to that of p) 13. When a dipole is placed at an angle θ from the direction of a uniform electric field E, it experiences a torque given by τ = pE sin θ or τ = × p E 14. Gauss’ law states that the surface integral of the electric field intensity over any closed surface (called Gaussian surface) in free space is equal to 1 0 ε times the net charge enclosed within the surface. φ ε ε E i n d qi q = ⋅ = = ∫ = E S 1 0 1 0 Σ where, q q i i n = i = = Σ 1 is the algebraic sum of all the charges inside the closed surface. 15. Electric field due to an infinitely long straight uniformly charged wire, E r = ε λ 2π 0 16. Electric field due to a thin infinite plane sheet of charge, E = ε σ 2 0 17. Electric field due to a uniformly charged thin spherical shell (i) Outside the shell, E q r = ε ⋅ 1 4 0 2 π (ii) Inside the shell, E = 0 1. While taking off synthetic clothes, seeing a spark or hearing a crackle, are due to (a) motion of ions through air (b) production of shock waves due to motion of electrons (c) electric discharge (d) cannot be explained 2. Out of gravitational, electromagnetic, van der Waals’, electrostatic and nuclear forces, which two are able to provide an attractive force between two neutrons? (a) Electrostatic and gravitational (b) Electrostatic and nuclear (c) Gravitational and nuclear (d) Some other forces like van der Waals’ 3. In general, metallic ropes are suspended from the carriers to the ground which take inflammable material. The reason is (a) their speed is controlled (b) to keep the gravity of the carrier nearer to the earth (c) to keep the body of the carrier in contact with the earth (d) nothing should be placed under the carrier 4. If a plastic rod rubbed with fur is made to touch two small pith balls suspended nearby, then which figure shows their final configuration? Electric Charge Topic 1 Objective Questions Based on NCERT Text (a) (b) (c) (d)
5. For the figure shown, the instrument (a) is used to measure quantity of a fluid (b) is used to measure wind velocity is called windmeter (c) is used to measure viscosity of a fluid (d) is used to detect presence of charge on a body, is called electroscope 6. When a body is connected to earth, electrons from the earth flow into the body. This means the body is ...... . (a) unchanged (b) charged positively (c) charged negatively (d) as insulator 7. One metallic sphere A is given positive charge whereas another identical metallic sphere B of exactly same mass as of A is given equal amount of negative charge. Then, (a) mass of A and mass of B still remain equal (b) mass of A increases (c) mass of B decreases (d) mass of B increases 8. A glass rod rubbed with silk is used to charge a gold leaf electroscope and the leaves are observed to diverge. The electroscope thus charged is exposed to X-rays for a short period. Then, (a) the divergence of leaves will not be affected (b) the leaves will diverge further (c) the leaves will collapse (d) the leaves will melt 9. Electric wiring in our houses has (a) only one wire : live (b) two wires : neutral, earth (c) three wires, live, neutral, earth (d) no wire 10. A soap bubble is given a negative charge, then its radius (a) decreases (b) increases (c) remains unchanged (d) nothing can be predicted as information is insufficient 11. If two bodies are rubbed and one of them acquires q1 charge and another acquires q2 charge, then ratio q q 1 2 : is (a) 1 : 2 (b) 2 : 1 (c) − 1 1: (d) 1 : 4 12. Two bodies are rubbed and one of them is negatively charged. For this body, if mi = initial mass, mf = mass after charging, then (a) m m i f = (b) m m i f < (c) m m i f > (d) m m m i f f + = 2 13. When we touch a pith ball with an electrified plastic rod, some of the negative charges on the rod are transferred to the pith ball and it also gets charged. Thus, pith ball is charged by (a) induction (b) contact (c) repulsion (d) None of these 14. In charging by induction, (a) body to be charged must be an insulator (b) body to be charged must be a semiconductor (c) body to be charged must be a conductor (d) any type of body can be charged by induction 15. Charge on a body is q1 and it is used to charge another body by induction. Charge on second body is found to be q2 after charging. Then, (a) q q 1 2 = 1 (b) q q 1 2 < 1 (c) q q 1 2 ≤ 1 (d) q q 1 2 ≥ 1 16. A body A is being charged by another charged body B by induction process. Then, charge acquired by A depends on (a) nature of material of A (b) distance between A and B (c) nature of medium separating A and B (d) All of the above 17. Additive nature of charge means (a) total charge on a system remains constant (b) total charge on an isolated system is always zero (c) charges are of two types positive and negative (d) it tells about the scalar nature of charge 18. Conservation of charge follows from law of conservation of mass. Above statement is (a) correct (b) incorrect (c) nothing can be said (d) mass and charge are two different physical quantities following conservation law 19. Charge of a body is always an integral multiple of (a) charge present in its one atom (b) charge present in one mole of material of body (c) charge present on an electron (d) charge of its one nucleus 20. The minimum charge on an object is (a) 1 C (b) 1 stat C (c) 1.6 10 19 × − C (d) 3.2 10 19 × − C Rubber Metal rod Glass bottle Gold leaves Ball (metal knob)
21. When a glass rod is rubbed with a silk cloth, charge appears on both. This observation is consistent with law of conservation of charge as (a) charge on both causes attraction (b) charge on both causes repulsion (c) charges appearing on both bodies are equal and opposite (d) charge on first body is more than that of second body 22. If a body gives out 109 electrons per second, how much time is required to get a total charge of 1 C from it? (a) Around 198 min (b) Around 198 h (c) Around 198 days (d) Around 198 yr 23. The number of electrons that must be removed from an electrically neutral silver dollar to give it a charge of + 2.4 C is (a) 2.5 × 1019 (b) 1.5 × 1019 (c) 1.5 × − 10 19 (d) 2.5 × − 10 19 24. An object of mass 1 kg contains 4 1020 × atoms. If one electron is removed from every atom of the solid, the charge gained by the solid of 1 g is (a) 2.8 C (b) 6.4 C × − 10 2 (c) 3.6 C × − 10 3 (d) 9.2 C × − 10 4 25. Magnitude of force between two point charges q1 and q2 which are separated by a distance r is given by (a) F k q q r = | | 1 2 (b) F k q q r r = | | 1 2 2 (c) F k q q r =       | 1 2 2 (d) F k q q r = | | ⋅ 1 2 2 26. Suppose charge on a metallic sphere is q. If the sphere is put in contact with an identical uncharged sphere, the charge will spread over the two spheres. By symmetry charge on each sphere will be ...... When distance between two charged spheres is varied so that it becomes half the initial distance, force between them will become ...... (a) q 2 , half (b) q 2 , four times (c) 2q, half (d) 2q, double 27. Force between two charges q1 and q2 separated by a distance r is proportional to q q r 1 2 2 / . Proportionality constant is (a) ε π 0 4 (b) 4π ε0 (c) 1 4π ε0 (d) 1 28. In the following configuration of charges, force on charge q2 by q1 is given by (a) F r 21 0 1 2 2 21 1 4 = ⋅ πε q q r $ (b) F r 21 0 1 2 2 21 1 4 = − πε q q r ( $ ) (c) F r 21 0 1 2 3 21 1 4 = ⋅ πε q q r $ (d) F r 21 0 1 2 3 21 1 4 = ⋅ − πε q q r ( $ ) (here, r r = = − | ) 21 2 1 r r 29. Fg and Fe represents gravitational and electrostatic force respectively between electron and proton at a distance of 10 cm. The ratio of F F g e / is of the order of (a) 1042 (b) 10−39 (c) 1 (d) 10−43 30. For charges q1 and q2 , if force between them for some separation in air is F, then force between them in a medium of permittivity ε will be (a) ε ε 0 F (b) ε ε0 F (c) εε0F (d) F ε ε0 31. Two identical charged spheres suspended from a common point by two massless strings of lengths l, are initially at a distance d (d < < 1) apart because of their mutual repulsion. The charges begin to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity v. Then, v varies as a function of the distance x between the sphere, as [NEET 2016] (a) v x ∝ (b) v x ∝ −1 2/ (c) v x ∝ −1 (d) v x ∝ 2 32. Suppose the spheres A and B with charge 6.5 10 C7 × − and distance between centres is 50 cm have identical sizes. A third sphere of the same size but uncharged is brought in contact with the first, then brought in contact with the second and finally removed from both. What is the new force of repulsion between A and B? (a) 5.7 10 N3 × − (b) 1.5 10 N2 × − (c) 0.24 N (d) 0.24 10 N2 × − Force between Two Charges : Coulomb’s Law Topic 2
33. The ratio of the forces between two small spheres with constant charge (a) in air (b) in a medium of dielectric constant K is (a) 1: K (b) K :1 (c) 1 2 : K (d) K 2 1: 34. Two point charges placed at a certain distance r in air exert a force F on each other. Then, the distance r′ at which these charges will exert the same force in a medium of dielectric constant K is given by (a) r (b) r K/ (c) r K / (d) r K 35. Two charges, each equal to q,are kept at x a x a = − = and on the X-axis.A particle of mass m and charge q q 0 2 = − is placed at the origin. If charge q0 is given a ,small displacement ( ) y a << along the Y -axis, the net force acting on the particle is proportional to [JEE Main 2013] (a) y (b) − y (c) 1 y (d) − 1 y 36. Two small spheres each having the charge +Q are suspended by insulating threads of length L from a hook. This arrangement is taken in space where there is no gravitational effect, then the angle between the two suspensions and the tension in each will be (a) 180 1 4 0 2 2 2 ° , πε ( ) Q L (b) 90 1 4 0 2 2 ° , πε Q L (c) 180 1 4 0 2 2 2 ° , πε Q L (d) 180 1 4 0 2 2 ° , πε Q L 37. Force between two charges varies with distance between them as 38. Two electrically charged particles, having charges of different magnitudes, when placed at a distance d from each other, experience a force of attraction F. These two particles are put in contact and again placed at the same distance from each other. What is the nature of new force between them? (a) Attractive (b) Repulsive (c) Attractive or repulsive depending upon magnitude of charges present on them (d) Cannot predicted 39. Three charges q q q 1 2 3 , and each of 1 C are at the vertices of an equilateral triangle of side l. Force on a charge q = 2μCplaced at the centroid of the triangle is (a) 3 N (b) 3 μN (c) zero (d) 3 10 2 × − N 40. If charges q q, and −q are placed at vertices of an equilateral triangle of side l.If F1 , F2 and F3 are the forces on the charges respectively, then (a) | | F F F 1 2 3 2 2 + + = 3 kq l (b) | | F F F 1 2 3 + + = 0 (c) | F F F 1 2 3 2 2 + + =| 3 2 kq l (d) |F F F | 1 2 3 2 2 + + = 2 kq l 41. Four charges q A = 2μC, qB = − 5μC, qC = 2μCand qD = − 5μC are placed at corners of a square ABCD of side 10 cm. What is the force on a charge of 1μC placed at centre of the square? (a) 10 10 7 × − N (b) 10 10 5 × − N (c) 10 10 3 × − N (d) Zero 42. Four charges equal to − Q are placed at the four corners of a square and a charge q is at its centre. If the system is in equilibrium, the value of q is (a) − + Q 4 1 2 2( ) (b) Q 4 1 2 2( ) + (c) − + Q 2 1 2 2( ) (d) Q 2 1 2 2( ) + F r (a) F r (b) F r (c) F r (d)