Hsslive XII Physics Chapter 1 (2025) PDF

Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® Chapter 1 Electric Charges and Fields 1.1 Introduction A common example of electric discharge is the lightning that we see in the...

Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® Chapter 1 Electric Charges and Fields 1.1 Introduction A common example of electric discharge is the lightning that we see in the sky during thunderstorms. We also experience a sensation of an electric shock either while opening the door of a car or holding the iron bar of a bus after sliding from our seat. The reason for these experiences is discharge of electric charges through our body, which were accumulated due to rubbing of insulating surfaces. This is due to generation of static electricity. Static means anything that does not move or change with time. Electrostatics deals with the study of forces, fields and potentials arising from static charges. 1.2 Electric charge Historically the credit of discovery of the fact that amber rubbed with wool or silk cloth attracts light objects goes to Thales of Miletus, Greece, around 600 BC. The name electricity is coined from the Greek word elektron meaning amber. If Two glass rods rubbed with wool or silk cloth are brought close to each other, they repel each other [Fig. 1.1(a)]. Similarly, two plastic rods rubbed with cat’s fur repelled each other [Fig. 1.1(b)]. On the other hand, the plastic rod attracts the glass rod [Fig. 1.1(c)]. There are two kinds of electrification and we find that (i) like charges repel and (ii) unlike charges attract each other. The property which differentiates the two kinds of charges is called the polarity of charge. --------------------------------------------------------------------------------------------- Seema Elizabeth, HSST physics, MARM GHSS Santhipuram  Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® The charges were named as positive and negative by the American scientist Benjamin Franklin. On rubbing electrons are transferred from one body to the other. The body, which loses electrons, will become positively charged and which gains electrons becomes negatively charged. When a glass rod is rubbed with silk, glass rod becomes positively charged and silk negative. When a plastic rod is rubbed with fur, plastic rod becomes negatively charged and fur positive. 1.3 Conductors and Insulators Conductors Conductors are those substances which allow passage of electricity through them. Eg. Metals, human and animal bodies and earth are conductors. They have electric charges (electrons) that are comparatively free to move inside the material. When some charge is transferred to a conductor, it readily gets distributed over the entire surface of the conductor. ▪ Metals cannot be charged by friction,because the charges transferred to the metal leak through our body to the ground as both are conductors of electricity. Insulators The substances which offer high resistance to the passage of electricity through them are called Insulators. Eg. glass, porcelain, plastic, nylon, wood ▪ If some charge is put on an insulator, it stays at the same place. So insulators gets electrified on combing dry hair or on rubbing. Gold Leaf Electroscope A simple apparatus to detect charge on a body is called a gold-leaf electroscope. Apparatus It consists of a vertical metal rod placed in a box. Two thin gold leaves are attached to its bottom end as shown in figure.  Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® Working When a charged object touches the metal knob at the top of the rod, charge flows on to the leaves and they diverge. The degree of divergence is an indicator of the amount of charge. 1.4 Basic properties of electric charges 1. Additivity of charge: The total charge on a surface is the algebraic sum of individual charges present on that surface. If a system contains n charges q1 , q 2 , q 3....................., q n then the total charge of the system is, 𝒒 = 𝒒𝟏 + 𝒒𝟐 + 𝒒𝟑 +.................. + 𝒒𝒏 2. Charge is conserved: It means that total charge of an isolated system remains constant. It s not possible to create or destroy net charge carried by an isolated system although the charge carrying particles may be created or destroyed in a process. 3. Quantization of charge : According to quantisation of electric charge, charge of a body is an integral multiple of a basic charge, which is the electronic charge. Charge on a body, q=± ne ; where, n=1,2,3......... e is the electronic charge. e=1.602 x 10−19 C Example 1 How many electronic charges form 1 C of charge? q=±ne, 𝑞 n= 𝑒 1 n= =6.25 x1018 1.602 x 10−19  Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® Example 2 A comb drawn through person’s hair causes 1022 electrons to leave the 2person’s hair and stick to the comb. Calculate the charge carried by the comb. q= ne, q = 1022 x 1.602 x 10−19 C = −1.602 x 103 C As the comb gains electrons it gets negatively charged. 1.5 Coulomb’s Law The force of attraction or repulsion between two stationery electric charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. 𝟏 𝐪𝟏 𝐪𝟐 If charges are placed in free space, 𝐅 = 𝟒𝛑𝛆 𝟎 𝐫𝟐 𝟏 𝐪𝟏 𝐪𝟐 If charges are placed in a medium, 𝐅 = 𝟒𝛑𝛆 𝟎 𝛆𝐫 𝐫𝟐 Definition of coulomb 𝟏 𝐪𝟏 𝐪𝟐 𝐅 = 𝟒𝛑𝛆 𝟎 𝐫𝟐 Coulomb’s Law in vector form  Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® 1.6 Forces between Multiple charges consider a system of three charges q1, q2 and q3 , as shown in figure. The force on one charge q1 , due to two other charges q2 , q3 is obtained by performing a vector addition of the forces due to each one of these charges. Super position principle Force on a charge due to a number of charges is the vector sum of forces due to individual charges. For a system of n charges, 1.7 Electric Field Electric field is the region around a charge where its effect can be felt. Intensity of electric field at a point is the force per unit charge. 𝐅 𝐄= 𝐪  Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® Electric field due to a point charge 1 qq0 By Coulomb’s law, F = 4πε 0 r2 F E=q 0 𝟏 𝐪 𝐄 = 𝟒𝛑𝛆 𝟐 𝟎𝐫 Electric field due to a system of charges Electric field at a point due to a system of charges is the vector sum of the electric fields at the point due to individual charges. 1.8 Electric Field Lines An electric field line is a curve drawn in such a way that the tangent to it at each point is in the direction of the net field at that point. ▪ Electric Field lines start from positive charge and end at negative charge. ▪ Electric field lines of a positive charge are radially outwards and that of a negative charge is radially inwards ▪ Electric field lines do not form closed loops. ▪ In a charge free region field lines are continuous. ▪ Two field lines never intersect.( Two directions for electric field is not possible at a point) ▪ Field lines are parallel ,equidistant and in same direction in uniform electric field.  Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® Positive Charge Negative Charge Two positive Charges Dipole - Positive and Negative charge 1.9 Electric Flux 𝛟 = ∫ 𝐄 ⋅ ⅆ𝐒 𝛟 = ∫ 𝐄 ⅆ𝐒 𝐜𝐨𝐬𝛉 ( 𝛉 𝐢𝐬 𝐭𝐡𝐞 𝐚𝐧𝐠𝐥𝐞 𝐛𝐞𝐭𝐰𝐞𝐞𝐧 𝐄 𝐚𝐧ⅆ 𝐧𝐨𝐫𝐦𝐚𝐥 𝐭𝐨 ⅆ𝐒)  Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® 1.10 Electric Dipole An electri dipole is a pair of equal and opposite charges separated by a distance The total charge of the system is +q + -q =0 ⃗) Electric Dipole moment (𝐩  Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® Electric Field due to a Dipole along the Axial Line The electric field at P due to +q 1 𝑞 𝐸+𝑞 = 4𝜋𝜀 (𝑟−𝑎)2 (in the direction of dipole moment 𝑝) 0 The electric field at Pdue to -q 1 𝑞 𝐸−𝑞 = 4𝜋𝜀 (𝑟+𝑎)2 (opposite to the direction of dipole moment 𝑝) 0 Total field, E =𝐸+𝑞 − 𝐸−𝑞 1 𝑞 1 𝑞 𝐸 = 4𝜋𝜀 (𝑟−𝑎)2 − (𝑟+𝑎)2 0 4𝜋𝜀0 Thus the total electric field at P is 𝑞 1 1 𝐸 = 4𝜋𝜀 [(𝑟−𝑎)2 − (𝑟+𝑎)2 ] 0 Simplifying 𝑞 4𝑎𝑟 𝐸 = 4𝜋𝜀 [(𝑟 2 −𝑎2 )2 ] 0 For r≫ 𝑎 ,we get 1 4𝑞𝑎 𝐸 = 4𝜋𝜀 [ 𝑟 3 ] 0 2qa=𝑝 (dipole moment) 𝟏 ⃗ 𝟐𝒑 ⃗𝑬 ⃗ = [ 𝟑] 𝟒𝝅𝜺𝟎 𝒓 Electric Field due to a Dipole along the Equatorial Line  Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® The magnitude of electric field at P due to +q 1 𝑞 𝐸+𝑞 = ----------------(1) 4𝜋𝜀0 𝑟 2 + 𝑎2 The magnitude of electric field at P due to -q 1 𝑞 𝐸−𝑞 = 4𝜋𝜀 ------------------(2) 0 𝑟 2 + 𝑎2 The vertical componennts cancel each other and horizontal components add up Total electric field at P, E =𝐸+𝑞 𝑐𝑜𝑠𝜃 + 𝐸−𝑞 𝑐𝑜𝑠𝜃 But , 𝐸+𝑞 = 𝐸−𝑞 E =2𝐸+𝑞 𝑐𝑜𝑠𝜃 --------------(3) 𝑎 𝑎 Cos𝜃= 2 2 = 2 2 1⁄ ---------------(4) √𝑟 +𝑎 (𝑟 +𝑎 ) 2 Substituting eq(1) and (4) in eq(3) 1 𝑞 𝑎 E =2 𝑥 2 2 𝑥 1 4𝜋𝜀0 𝑟 +𝑎 (𝑟 2 +𝑎2 ) ⁄2 p=2qa (dipole moment) 1 𝑝 𝐸 = 4𝜋𝜀 [(𝑟 2 +𝑎2 )3/2 ] 0 For r≫ 𝑎 ,we get 𝟏 ⃗ 𝒑 ⃗𝑬 ⃗ = [ 𝟑] 𝟒𝝅𝜺𝟎 𝒓 Relation connecting Axial field and Equatorial field of a Dipole 1 2𝑝 Axial field, 𝐸⃗ = [ 3] 4𝜋𝜀0 𝑟 1 𝑝 Equatorial field , 𝐸⃗ = [ ] 4𝜋𝜀0 𝑟 3 Axial field = 2 x Equatorial field 1.11 Dipole in a Uniform External field In a uniform electric field there will be a net torque on the dipole, but the net force will be zero. Due to the torque ,the dipole rotates. There will be no translatory motion as the net force is zero. Torque on a Dipole in a Uniform External field  Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® Torque, τ = one of the forces x perpendicular distance between them. τ = qE x 2a sinθ τ =pE sinθ 𝛕=𝐏 ⃗ ×𝐄 ⃗ When p and E are in the same direction or opposite direction( θ=0 or180 ) τ =pE sin0 =0 Torque is maximum , when p and E are perpendicular. (θ=90) τ =pE sin90 =pE Dipole in a non uniform electric field In a non uniform electric field the dipole experiences a net force as well as a net torque in general. Case 1 -when p is parallel to E when p is parallel to E, the dipole has a net force in the direction of increasing field. But the net torque will be zero τ =pE sin0 =0 Case 2-When p is antiparallel to E. When p is antiparallel to E, the net force on the dipole is in the direction of decreasing field. But the net torque will be zero, τ =pE sin 180 =0  Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® 1.12 Continuous Charge Distribution Linear charge density The linear charge density λ of a wire is defined as 𝛥𝑞 𝜆= 𝛥𝑙 𝒒 𝝀= 𝒍 The unit of λ is C/m Line charge q = 𝝀𝒍 Surface charge density The surface charge density 𝜎 of a area element is defined as 𝛥𝑞 𝜎= 𝛥𝑆 𝒒 𝝈=𝑺 The units for σ is C/𝑚2 Surface charge, q= 𝝈𝑺 Volume charge density The volume charge density ρ of a volume element is defined as 𝛥𝑞 ρ= 𝛥𝑉 𝒒 𝛒=𝑽 The units for ρ is C/𝑚3 Volume charge , q= 𝛒𝑽 1.13 Gauss’s Law Gauss’s law states that the total electric flux through a closed surface is 𝟏 equal to times the total charge enclosed by the surface. 𝜺𝟎 𝒒 𝝓 = ∮ 𝑬 ⋅ ⅆ𝑺 = 𝜺 𝟎 The surface over which we calculate the flux is called Gaussian surface.  Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® Proof Consider a sphere of radius r enclosing a point charge q. the electric flux through the surface dS ϕ = ∫ E ⋅ dS ϕ = ∫ E dS cos0 = ∫ E dS =𝐸∫ dS ϕ = ES 1 q ϕ = x 4πr 2 4πε0 r2 𝐪 𝛟=𝛆 𝟎 Features of Gauss’s Law Gauss’s law is true for any surface irrespective of the size and shape. The charge includes the sum of all charges enclosed by the surface. The surface that we choose for the application of Gauss’s law is called the Gaussian Surface. Gauss’s law is applicable to both symmetric and asymmetric system, but it will be much easier if the system has some symmetry. Gauss’s law is based on inverse square dependence on distance contained in the Coulomb’s law. Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® 𝟏. 𝟏𝟒 Applications of Gauss’s Law Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® c) field inside the shell ϕ = ES (1) Inside the shell q=0 ES=0 (S≠ 𝟎)  Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ® Example Find the electric field due two plane sheets of charge in regions I ,II and III `