electric charges and fields class 12 study material pdf download
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The document discusses electrostatics, focusing on electric charges, their properties, and interactions, including methods of charging bodies such as by rubbing, induction, and conduction. It covers fundamental concepts like Coulomb's law, the electric field, and electric dipoles, explaining their significance and practical applications in various fields. Additionally, it highlights the principles of charge conservation and quantization, emphasizing the importance of electric forces in daily life and technology.
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electric charges and fields class 12 study material pdf download
- 1. ELECTRIC CHARGES AND FIELDS Introduction The Greek word for amber is “elektron”; this is the origin of the terms electricity and electron. Electrostatic is a branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges with no acceleration. While it’s hard to see the electric charges that are responsible for electricity, it’s easy to see their effects. They’re all around us: in the sparks and shocks of a cold winter day, the imaging process of a xerographic copier, and the illumination of a flashlight when you turn on its switch. Although we often take electricity for granted, it clearly underlies many aspects of our modern world. Just imagine what life would be like if there were no electric charges and no electricity. For starters, we’d probably be sitting around campfires at night, trying to think of things to do without television, cell phones, or computer games. But before you remark on just how peaceful such a pre-electronic-age existence would be, let me add one more sobering thought: we wouldn’t exist either. Whether it’s motionless as static charge or moving as electric current, electricity really does make the world go ‘round. Electricity may be difficult to see, but you can easily observe its effects. How often have you found socks clinging to a shirt as you remove them from a hot dryer or struggled to throw away a piece of plastic packaging that just won’t leave your hand or stay in the trash can? The forces behind these familiar effects are electric in nature and stem from what we commonly call “static electricity.” Static electricity does more than just push things around, however, as you’ve probably noticed while reaching for a doorknob or a friend’s hand on a cold, dry day. In this section, we’ll examine static electricity and the physics behind its intriguing forces and often painful shocks. When a plastic comb is rubbed with your hairs, it acquires the property of attracting light objects such as paper pieces. What we study under electrostatics is static electricity. The charges at rest develop due to friction when we rub two insulating bodies against each other. Some industrial applications of electrostatics are: 1. In designing electrostatics generators like Van de Graff generator 2. In electrostatic spraying of paints, powders etc. All right copy reserved. No part of the material can be produced without prior permission
- 2. 3. In the design of cathode ray tubes for radar, television etc. 4. Ink-jet printing 5. Understanding lightning that strikes from the cloud base to the ground. 6. Adhesive forces of glue associated with surface tension, all are electric in nature Methods of charging There are three main methods for charging of a body (i) Charging by rubbing and Frictional electricity:- Rubbing as the term suggest is moving two things back and forth against each other. The simplest way to experience electric charge is to rub certain bodies among each other. Rubbing or friction makes electrons move. This gives one material a positive charge and the other a negative charge. The charges stay on the surfaces of the materials until they can flow or they discharge. If we pass a comb through hairs, comb becomes charged and can attract small pieces of paper. This is because the comb might have lost its electrons or acquired some electrons when we rub it with hairs. Now, this comb is a charged body. The net charge on the comb interacts with the net charge on small pieces of paper which results in attraction. Many such solid materials are known which on rubbing attract light objects like a light feather, bits of papers, straw etc. Explanation of appearance of electric charge on rubbing is simple. Material bodies consist of a large number of electrons and protons in equal number and hence is in neutral in their normal state. But when a glass rod is rubbed with a silk cloth, electrons are transferred from glass rod to silk cloth. The glass rod becomes positively charged and the silk cloth becomes negatively charged as it receives extra electrons from the glass rod. In this case rod after rubbing, comb after passing through dry hairs becomes electrified and these are the example of frictional electricity. (ii) Charging by induction (Electrostatic Induction):- The temporary electrification of a conductor, when a charged body is brought near it is called electrostatic induction. All right copy reserved. No part of the material can be produced without prior permission
- 3. Electrostatic Induction: - Electrical charges in the conductor are redistributed When a body is charged this way there is no transfer of electrons from one body to other. This happens because there is no physical contact taking place between charging body and conductor being charged. If a charged body is brought near an uncharged body, then the neutral body becomes oppositely charged. By induction method, we can charge any type of material body. (iii) By conduction (by touch without rubbing):- Because of having excess free electrons in metals they can be charged by conduction. When we bring two conductors, one charged and other uncharged in contact, the same type of charge will appear on both the conductors. Basic properties of electric charge Additivity of charges The total charge of an isolated system is equal to an algebraic sum of individual charges of the system. For example, the total charge of a system containing five charges +1, +2, –3, +4 and – 5, in some arbitrary unit, is (+1) + (+2) + (–3) + (+4) + (–5) = –1 in the same unit. Conservation of charge The total charge of an isolated system is always conserved that means charge can neither be created nor be destroyed but can be transferred from one body to another. When bodies are charged by rubbing, there is transfer of electrons from one body to the other; no new charges are either created or destroyed. Quantisation of charge Any charged body has a total charge ± ne where ‘n` is an integer (n =0, 1, 2, 3………..). This experimental fact is called quantisation of charge. q = ± ne, where n is an integerand e = 1.6 × 10 - 19 C By convention, the charge on an electron is taken to be negative; therefore charge on an electron is written as –e and that on a proton as +e. The SI unit of charge is Coulomb and is denoted by the symbol C. All right copy reserved. No part of the material can be produced without prior permission
- 4. 1𝞵C=10 -6 C At the macroscopic level, one deals with charges that are enormous compared to the magnitude of charge e. A charge of magnitude, say 1 μC, contains something like 10 13 times the electronic charge. At this scale, the fact that charge can increase or decrease only in units of e. Thus, at the macroscopic level, the quantisation of charge has no practical consequence and can be ignored. At the microscopic level, where the charges involved are of the order of a few tens or hundreds of e, i.e., they can be counted and quantisation of charge cannot be ignored. Coulomb's Law In 1785 the French physicist Charles Augustin Coulomb measured the electric force between small charged spheres using a torsion balance. He then formulated his observations in the form of Coulomb's Law. Coulomb's Law is an electrical analog of Newton's Universal Law of Gravitation. It states that The force of attraction or repulsion between two stationary point charges is (i) directly proportional to the product of the magnitude of two charges. (ii) Inversely proportional to the square of the distance between them. This force acts along the line joining the two charges. To explain above statement consider the figure given below Coulomb's Law Above figure consists of two point charges q1 and q2. These two charges are separated by a distance r. Then according to Coulomb's Law, F α 𝑞1𝑞2 𝑟2 F= k 𝑞1𝑞2 𝑟2 k= 1 4𝞹𝟄0 𝟄0 is called permittivity of air or free space. (absolute permittivity) F= 1 4𝞹𝟄0 𝑞1𝑞2 𝑟2 Value of 𝟄0= 8.85x10 -12 𝑐2 𝑁𝑚2 All right copy reserved. No part of the material can be produced without prior permission
- 5. 1 4𝞹𝟄0 = 9x10 9 𝑁𝑚2 𝐶2 F= 1 4𝞹𝟄0 𝑞1𝑞2 𝑟2 F = 9x10 9 𝑞1𝑞2 𝑟2 If the charges are placed in a medium of permittivity 𝟄 F= 1 4𝞹𝟄 𝑞1𝑞2 𝑟2 Relative permittivity Or Dielectric constant (K Or 𝟄�r) It is the ratio of permittivity of a medium to the permittivity of free space. 𝟄 r = 𝟄 𝟄0 𝟄= 𝟄 0 𝟄 r F= 1 4𝞹𝟄 𝑞1𝑞2 𝑟2 F= 1 4𝞹𝟄0𝟄𝑟 𝑞1𝑞2 𝑟2 OR F= 1 4𝞹𝟄0𝐾 𝑞1𝑞2 𝑟2 UNIT OF CHARGE- COULOMB F= 1 4𝞹𝟄0 𝑞1𝑞2 𝑟2 F = 9x10 9 𝑞1𝑞2 𝑟2 If q 1 =q 2 = 1C and r=1m F = 9x10 9 N 1 Coulomb is that charge when placed in air or vacuum at a distance of 1m from an equal and similar charge experiences a force of 9x10 9 N. Coulomb’s law in vector form Force on q 2 due to q 1, 𝐹21 ̅̅̅̅̅ = 1 4𝞹𝟄0 𝑞1𝑞2 𝑟2 𝑟12 ̂ 𝑟12 ̂ Is the unit vector pointing from q 1 to q 2 All right copy reserved. No part of the material can be produced without prior permission
- 6. 𝑟12 ̂ = 𝑟12 ̅̅̅̅̅ 𝑟 𝐹21 ̅̅̅̅̅ = 1 4𝞹𝟄0 𝑞1𝑞2 𝑟3 𝑟12 ̅̅̅̅̅ Force on q 1 due to q 2, 𝐹12 ̅̅̅̅̅ = 1 4𝞹𝟄0 𝑞1𝑞2 𝑟2 𝑟21 ̂ 𝑟21 ̂ is the unit vector pointing from q 2 to q 1 𝑟21 ̂ = 𝑟21 ̅̅̅̅̅ 𝑟 𝐹12 ̅̅̅̅̅ = 1 4𝞹𝟄0 𝑞1𝑞2 𝑟3 𝑟21 ̅̅̅̅̅ 𝑟12 ̅̅̅̅= - 𝑟21 ̅̅̅̅ 𝐹12 ̅̅̅̅= - 𝐹21 ̅̅̅̅ ie Coulomb’s law obey Newton’s third law Principle of Superposition Principle of superposition gives the method to find force on a charge when system consists of large number of charges. According to this principle when multiple charges are interacting the total force on a given charge is vector sum of forces exerted on it by all other charges. This principle makes use of the fact that the forces with which two charges attract or repel one another are not affected by the presence of other charges. If a system of charges has n number of charges say q1, q2,...................., qn, then total force on charge q1 according to principle of superposition is 𝐹. ̅ = 𝐹12 � ̅̅̅̅̅̅+𝐹13 ̅̅̅̅̅ +………………….𝐹1𝑛 ̅̅̅̅̅ As per the principle of superposition, the force on any charge due to a number of other charges is the vector sum of all the forces on that charge due to other charges, taken one at a time. All right copy reserved. No part of the material can be produced without prior permission
- 7. 𝐹12 ̅̅̅̅̅ = 1 4𝞹𝟄0 𝑞1𝑞2 𝑟122 𝑟12 ̂ 𝐹13 ̅̅̅̅̅ = 1 4𝞹𝟄0 𝑞1𝑞2 𝑟132 𝑟13 ̂ 𝐹1 ̅̅̅̅ = 𝐹12 � ̅̅̅̅̅̅+𝐹13 ̅̅̅̅̅ In case of n charges 𝐹. ̅ = 𝐹12 � ̅̅̅̅̅̅+𝐹13 ̅̅̅̅̅ +………………….𝐹1𝑛 ̅̅̅̅̅ ELECTRIC FIELD All right copy reserved. No part of the material can be produced without prior permission
- 8. The electric field is defined as the region or space around a charge where an electric force of attraction or repulsion can be experienced. Electric field Intensity Consider a charge Q placed in vacuum. If we place another point charge q at a point P, then the charge Q will exert a force on q as per Coulomb’s law. Let F ̅ be the force experienced by the charge q. Force experienced by unit charge, E ̅ = F ̅ q The electric field or field intensity at a point is defined as the force experienced by unit positive charge placed at that point. E ̅ = lim 𝑞→𝑜 � F ̅ q Significance of lim 𝑞→𝑜 � F ̅ q is that the test charge q should be negligibly small so that the source charge Q remain at its original position. Unit Electric field Intensity is N/C or V/m Electric field Intensity is a vector quantity. The force acting on the charge q is 𝐹 ̅= q𝐸 ̅ Physical Significance of electric field It is very important concept in understanding various electrostatic phenomenon. The space around every electric charge or electrically charged body is filled with an electric field thereby altering the space around it. This is the reason why electrostatic force like gravitational force is an action-at-a-distance force. Electric field should not be thought of as a kind of matter filled in space surrounding electric charge. It is a kind of aura or the distinctive atmosphere or quality that seems to surround and be generated by an electric charge. Electric field intensity due to a point charge All right copy reserved. No part of the material can be produced without prior permission
- 9. Consider a point P at a distance r from a point charge +q. Electric field intensity at the point P, Let us imagine a test charge q0 to be placed at P. Now we find force on charge q0 due to q through Coulomb's law. F ̅ = 1 4𝝿𝞊0 qq0 r2 r ̂ Electric field at point P, E ̅ = F ̅ q = 1 4𝝿𝞊0 q r2 r ̂ E ̅ = 1 4𝝿𝞊0 q r2 r ̂ Magnitude of Electric Field, E = 1 4𝝿𝞊0 q r2 Electric Field in terms of position vectors Electric dipole and Electric Dipole moment Electric dipole is a pair of equal and opposite charges, +q and −q, separated by a very small distance. Total charge of the dipole is zero but electric field of the dipole is not zero as charges q and -q are separated by some distance and electric field due to them when added is not zero. Dipole moment is the product of one of the charges and distance between them. 𝑃 ̅ = q 2𝑎 ̅ ̅ ̅ ̅ The unit of electric dipole moment is coulomb – meter (C-m) Electric dipole moment is a vector quantity and by convention, its direction is from –q to +q. All right copy reserved. No part of the material can be produced without prior permission
- 10. Examples of electric dipole:- Dipoles are common in nature. Molecules like H2O, HCl, and CH3COOH are electric dipoles and have permanent dipole moments. They have permanent dipole moments because the center of their positive charges does not fall exactly over the center of their negative charges. Figure given below shows molecule of water. Physical significance of Electric Dipole and dipole moment Atoms as a whole are electrically neutral in their ground state. We know that atoms have equal amount of positive and negative charge. Similar to atoms molecules are also neutral but they also have equal amount of positive and negative charges. Now when in a system, algebraic sum of all the charges is zero it does not necessarily mean that electric field produced by the system is zero everywhere. This makes study of electric dipoles important for electrical phenomenon in matter. Matter which is made up of atoms and molecules is electrically neutral. If the center of mass of positive charges coincides with that of negative charges then molecule behaves as non-polar molecule. On the other hand, if center of mass of positive charges does not coincides with that of negative charges then molecule behaves as polar molecule. These polar molecules have permanent dipole moments. These dipole moments are randomly oriented in the absence of external electric field. If we place a material with polar molecules in external electric field then these molecules align themselves in the direction of the field. This results in the development of a net dipole moment. This particular piece of material is said to be polarized. So study of dipole and dipole moments gives a measure of the polarization of a net neutral system. The study of dipole moments measures the tendency of a dipole to align with an external electric field. All right copy reserved. No part of the material can be produced without prior permission
- 11. Electric field of a dipole (On axial line) Consider a dipole of charge q and length 2a. Let P be a point at a distance x from the centre of the electric dipole. Electric field intensity at the point P due to the charge +q, E1= 1 4𝞹𝟄0 𝑞 (𝑥−𝑎)2 along BP Electric field intensity at the point P due to the charge -q, E2 = 1 4𝞹𝟄0 𝑞 (𝑥+𝑎)2 along PA The total electric field at P due to the dipole is E = E1 - E2 E = 1 4𝞹𝟄0 𝑞 (𝑥−𝑎)2 − 1 4𝞹𝟄0 𝑞 (𝑥+𝑎)2 E = 𝑞 4𝞹𝟄0 ( 1 (𝑥−𝑎)2 - 1 (𝑥+𝑎)2 ) E = 𝑞 4𝞹𝟄0 ( (𝑥+𝑎)2−(𝑥−𝑎)2 (𝑥2−𝑎2)2 ) E = 𝑞 4𝞹𝟄0 ( 4𝑎𝑥 (𝑥2−𝑎2)2 a<<x (a 2 can be neglected) E = 𝑞 4𝞹𝟄0 4𝑎𝑥 𝑥4 E = 𝑞 4𝞹𝟄0 4𝑎 𝑥3 All right copy reserved. No part of the material can be produced without prior permission
- 12. E = 1 4𝞹𝟄0 2(2𝑎𝑞) 𝑥3 E = 1 4𝞹𝟄0 2p 𝑥3 p=2𝑎𝑞(Electric dipole moment) Electric field of a dipole (On equatorial line line) The electric field at P due to the charge +q, E1= 1 4𝞹𝟄0 𝑞 𝑟2 along BP E 1 Can be resolved into two components E 1 Cos𝞱 and E 1 Sin𝞱. The electric field at P due to the charge -q, E2= 1 4𝞹𝟄0 𝑞 𝑟2 along PA E 2 Can also be resolved into two components E 2 Cos and E 2 Sin𝞱. Here Sin𝞱 components are equal and opposite, therefore they cancel out. But Cos𝞱 components are in the same direction, they can be added up. The total electric field at P due to the dipole, E = E 1 Cos𝞱 + E 2 Cos𝞱 E = 1 4𝞹𝟄0 𝑞 𝑟2 Cos𝞱 + 1 4𝞹𝟄0 𝑞 𝑟2 Cos𝞱 E = 2 1 4𝞹𝟄0 𝑞 𝑟2 Cos𝞱 Cos𝞱= a/r All right copy reserved. No part of the material can be produced without prior permission
- 13. E = 2 1 4𝞹𝟄0 𝑞 𝑟2 𝑎 𝑟 E = 1 4𝞹𝟄0 2𝑎𝑞 𝑟3 E = 1 4𝞹𝟄0 2𝑎𝑞 𝑟3 2aq=p E = 1 4𝞹𝟄0 p 𝑟3 𝑟 = (𝑥2 + 𝑎2 )1/2 E = 1 4𝞹𝟄0 p (𝑥2+𝑎2)3/2 if the length of the dipole is very small 𝑎2 can be neglected E = 1 4𝞹𝟄0 p 𝑥3 Torque acting on a dipole in an electric field Consider a dipole of charge q and length 2a placed in a uniform electric field E makes an angle 𝞱 with the direction of electric field. The charges +q and –q experience forces + qE and –qE respectively. These two equal and unlike forces constitute a couple. The net force acting on the dipole + qE- qE = 0 Torque(τ) = force x Perpendicular distance τ = qE x BN Sin𝞱= 𝐵𝑁 2𝑎 BN= 2a Sin𝞱 τ = qE x 2a Sin𝞱 τ = 2aqE Sin𝞱 2aq=p τ = PE Sin𝞱 In vector form, All right copy reserved. No part of the material can be produced without prior permission
- 14. ��τ ̅ =P ̅ X E ̅ Direction of torque is perpendicular to the plane containing dipole axis and electric field. Electric field lines Electric field is a vector quantity and can be represented as we represent vectors. Let us try to represent E due to a point charge pictorially. Let the point charge be placed at the origin. Draw vectors pointing along the direction of the electric field with their lengths proportional to the strength of the field at each point. Since the magnitude of electric field at a point decreases inversely as the square of the distance of that point from the charge, the vector gets shorter as one goes away from the origin, always pointing radially outward. Figure shows such a picture. In this figure, each arrow indicates the electric field, i.e., the force acting on a unit positive charge, placed at the tail of that arrow. Connect the arrows pointing in one direction and the resulting figure represents a field line. Now the magnitude of the field is represented by the density of field lines. E is strong near the charge, so the density of field lines is more near the charge and the lines are closer. Away from the charge, the field gets weaker and the density of field lines is less, resulting in well-separated lines. All right copy reserved. No part of the material can be produced without prior permission
- 15. The electric field lines are imaginary lines drawn in such a way that the tangent to which at any point gives the direction of the electric field at that point. Electric field lines of a single positive Charge Electric field lines of a single negative Charge The field lines of a single positive charge and a single negative The field lines of a single positive charge are radially outward while those of a single negative charge are radially inward. All right copy reserved. No part of the material can be produced without prior permission
- 16. Field lines around the system of two positive charges Field lines around the system of two positive charges gives a different picture and describe the mutual repulsion between them. Field lines around a system of a positive and negative charge (Electric dipole) All right copy reserved. No part of the material can be produced without prior permission
- 17. Field lines around a system of a positive and negative charge clearly shows the mutual attraction between them. Uniform electric field Electric field corresponding to a negative charge is placed with in the vicinity of a metal plate Properties of Electric field lines. 1) Electric field lines start from +ve charge and end in –ve charge. 2) Electric field lines do not form any closed loop. 3) Electric field lines never intersect each other. If two lines intersect at a point, it means two directions for the field at that point which is not at all possible and hence they never intersect each other. All right copy reserved. No part of the material can be produced without prior permission
- 18. 4) If the field lines are crowded, then the field is strong and if the field lines are not crowded, then field is weak. 5) The electric field lines are always normal to the surface of the charge body. 6) In a charge-free region, electric field lines can be taken to be continuous curves without any breaks. Electric flux (ϕ) The number of field lines crossing a unit area, placed normal to the field at a point is a measure of the strength of electric field at that point. This means that if we place a small planar element of area ΔS normal to E at a point, the number of field lines crossing it is proportional* to E ΔS. Now suppose we tilt the area element by angle θ. Clearly, the number of field lines crossing the area element will be smaller. The projection of the area element normal to E is ΔS cosθ. Thus, the number of field lines crossing ΔS is proportional to E ΔS cosθ. The electric flux is defined as the measure of total number of electric field lines passing normally through a given surface. If the surface is perpendicular to the field, then the flux through an area ΔS is Δϕ = E ΔS If the normal to the coil makes an angle 𝞱 with the electric field, Flux through the surface Δϕ = E ΔS Cos 𝞱 Δϕ = E. ΔS All right copy reserved. No part of the material can be produced without prior permission
- 19. Total Flux through a given surface ϕ =𝞢 E . ΔS OR ϕ = E . S Unit of electric flux is Nm 2 /C Electric field due to continuous charge distributions If a charge q is uniformly distributed along a line of length L, the linear charge density λ is defined by 𝞴 = 𝑞 𝐿 and the unit of λ is Coulomb/meter(C/m). For a charge q uniformly distributed over a surface of area A, the surface charge density σ is 𝞼 = 𝑞 𝐴 and unit of surface charge density is C/m2. Similarly for uniform charge distributions volume charge density is 𝞺 = 𝑞 𝑣 and unit of volume charge distribution is C/m3. GAUSS’S LAW Gauss's law was suggested by Karl Frederich Gauss (1777-1855) who was German scientist and mathematician. Gauss's law is basically the relation between the charge distribution producing the electrostatic field to the behaviour of electrostatic field in space. Gauss's law is based on the fact that flux through any closed surface is a measure of total amount of charge inside that surface and any charge outside that surface would not contribute anything to the total flux. All right copy reserved. No part of the material can be produced without prior permission
- 20. Gauss‘s law state that the total electric flux or total number of field lines passing through any closed surface is equal to 1 𝟄0 times the charges enclosed by the surface. ϕ = 𝑞 𝟄0 E . S = 𝑞 𝟄0 The electric flux through the surface = E . S The electric field intensity at P, E= 1 4𝞹𝟄0 𝑞 𝑟2 Surface area of the spherical surface, S = 4𝞹�r 2 The electric flux through the surface = E . S = 1 4𝞹𝟄0 𝑞 𝑟2 x 4𝞹�r 2 E S = 𝑞 𝟄0 ϕ = 𝑞 𝟄0 ie Gauss’s Law All right copy reserved. No part of the material can be produced without prior permission
- 21. APPLICATIONS OF GAUSS’S LAW Field due to an infinitely long straight uniformly charged wire. Consider an infinitely long thin straight wire with uniform linear charge density λ. Let P be a point at a distance r from the straight wire. The electric field lines are radially outward. To find the electric field intensity at P, imagine a Gaussian surface of radius r. The electric flux through two flat surfaces is zero because the electric field lines are radially outward. The electric flux through though the curved surface, E . S = 𝑞 𝟄0 E S = 𝑞 𝟄0 q = 𝞴�l S = 2𝞹�rl E 2𝞹�rl = λl 𝟄0 E = λ 2πr𝟄0 E ̅ = λ 2πr𝟄0 𝑛 ̂ where ˆn is the radial unit vector plane normal to the wire. Electric Flux ϕ = 𝑞 𝟄0 All right copy reserved. No part of the material can be produced without prior permission
- 22. ϕ = λl 𝟄0 Field due to a uniformly charged thin spherical shell (i) Field outside the shell Consider a spherical shell of radius R with uniform surface charge density 𝞼. Let P be a point at a distance r from the centre of the spherical shell. Here the electric field lines are radially outward. To find the electric field intensity at P imagine a Gaussian surface of radius r. Electric flux through the surface, E . S = 𝑞 𝟄0 E S = 𝑞 𝟄0 q = 4𝞹�R 2 𝞼� S = 4𝞹�r 2 E 4𝞹�r 2 = 4πR 2 σ 𝟄0 E = σR 2 𝟄0r2 If the point is on the surface of the charged spherical shell, r =R All right copy reserved. No part of the material can be produced without prior permission
- 23. E = σ 𝟄0 Field inside the shell If the point P is inside the Shell, the Gaussian surface is again a sphere through P centred at O. The flux through the Gaussian surface, E . S = 𝑞 𝟄0 Here the charge enclosed by the Gaussian surface is zero. (q = 0) E . S = 0 E =0 The electric field inside a charged spherical shell is zero Variation of electric field with distance from the centre of the spherical shell All right copy reserved. No part of the material can be produced without prior permission
- 24. Field due to a uniformly charged infinite plane sheet Consider an infinite plane sheet of charge with uniform charge density 𝞼. To find the electric field intensity at P, imagine a Gaussian cylinder of cross sectional area A normal to the plane of the sheet. Since the electric field lines are parallel to the curved surface, the flux through this surface is zero. The flux through two flat surfaces, E . S = 𝑞 𝟄0 E S = 𝑞 𝟄0 S = 2ΔS q =𝞼� ΔS E 2ΔS = σ ΔS 𝟄0 E = σ 2𝟄0 E = σ 2𝟄0 𝑛 ̂ E is independent of x All right copy reserved. No part of the material can be produced without prior permission
- 25. Electric field between two parallel plates In region I E = - ( σ 2𝟄0 + −σ 2𝟄0 )=0 In region II E = ( σ 2𝟄0 − −σ 2𝟄0 ) E = 2σ 2𝟄0 E = σ 𝟄0 Electric field intensity between two parallel plates E = σ 𝟄0 In region III E = ( σ 2𝟄0 + −σ 2𝟄0 )=0 All right copy reserved. No part of the material can be produced without prior permission