Page 1 1 UNIT - 11 ELECTROSTATICS Page 2 1 UNIT - 11 ELECTROSTATICS 2 SUMMARY 1. Electric Charge : Just as masses of two particles are responsible for the gravitational force, charges are responsible for the electric force. Electric charge is an intrinsic property of a particle. Charges are of two types : (1) Positive charges (2) Nagative charges. The force acting between two like charges is repulsive and two unlike charges it is attractive between . 2. Quantization of Electric Charge : The magnitude of all charges found in nature are an integral multiple of a fundamental charge. , ne Q ? where e is the fundamental unit of charge. 3. Conservation of Electric Charge : Irrespective of any process taking place, the algebraic sum of electric charges in an electrically isolated system always remains constant. 4. Coulomb's Law : The electric force between two stationary point charges is directly propor- tional to the product of their charges and inversely proportional to the square of the distance between them. 2 2 1 0 2 2 1 r q q 4 1 r q q k F ? ? ? ? If 0 q q 2 1 ? then there is a repulsion between the two charges and for 0 q q 2 2 ? , there is a attrac- tion between the charges. 5. Equation for Force using Columbâ€™s Law, when two charges are placed in a medium having dielectric constant k. (1) The electric force ? ? F experienced by a test charge (q 0 ) due to a source charge (q) when both are placed in a medium having dielectric constant k and separated by a dis- tance r, is given by : r Ë† kr q q 4 1 F 2 2 1 0 ? ? ? F r P O (q) (q o ) Here r Ë† is the unit vector directed from q to q 0 . (2) The equation of coulomb's force may be written as follows : ? ? r Ë† r k q q 4 1 F 2 2 1 0 ? ? ? (3) If the source charge and test charge are separated by a number of medium of thickness 1 2 3 d , d , d ........ having dielectric constants ........ k , k , k 3 2 1 respectively, then the electric force on charge q 0 due to a charge q is given by ? ? 0 2 2 2 0 1 1 2 2 3 3 qq 1 Ë† F r 4 k d k d k d ? ? ? ? ? ? 0 2 0 i i qq 1 Ë† F r 4 k d ? ? ? ? ? ? ? ? OR ? In this equation k i is dielectric constant of medium which spreads through the distance d i along the line joining q and q 0 . Page 3 1 UNIT - 11 ELECTROSTATICS 2 SUMMARY 1. Electric Charge : Just as masses of two particles are responsible for the gravitational force, charges are responsible for the electric force. Electric charge is an intrinsic property of a particle. Charges are of two types : (1) Positive charges (2) Nagative charges. The force acting between two like charges is repulsive and two unlike charges it is attractive between . 2. Quantization of Electric Charge : The magnitude of all charges found in nature are an integral multiple of a fundamental charge. , ne Q ? where e is the fundamental unit of charge. 3. Conservation of Electric Charge : Irrespective of any process taking place, the algebraic sum of electric charges in an electrically isolated system always remains constant. 4. Coulomb's Law : The electric force between two stationary point charges is directly propor- tional to the product of their charges and inversely proportional to the square of the distance between them. 2 2 1 0 2 2 1 r q q 4 1 r q q k F ? ? ? ? If 0 q q 2 1 ? then there is a repulsion between the two charges and for 0 q q 2 2 ? , there is a attrac- tion between the charges. 5. Equation for Force using Columbâ€™s Law, when two charges are placed in a medium having dielectric constant k. (1) The electric force ? ? F experienced by a test charge (q 0 ) due to a source charge (q) when both are placed in a medium having dielectric constant k and separated by a dis- tance r, is given by : r Ë† kr q q 4 1 F 2 2 1 0 ? ? ? F r P O (q) (q o ) Here r Ë† is the unit vector directed from q to q 0 . (2) The equation of coulomb's force may be written as follows : ? ? r Ë† r k q q 4 1 F 2 2 1 0 ? ? ? (3) If the source charge and test charge are separated by a number of medium of thickness 1 2 3 d , d , d ........ having dielectric constants ........ k , k , k 3 2 1 respectively, then the electric force on charge q 0 due to a charge q is given by ? ? 0 2 2 2 0 1 1 2 2 3 3 qq 1 Ë† F r 4 k d k d k d ? ? ? ? ? ? 0 2 0 i i qq 1 Ë† F r 4 k d ? ? ? ? ? ? ? ? OR ? In this equation k i is dielectric constant of medium which spreads through the distance d i along the line joining q and q 0 . 3 For example, see the figure below : Here, the space between the charges q and q 0 is filled with medium (1, 2, 3). The thickness of medium 1 is d 1 and its dielectric consant is k 1 Similarly the thickness of medium 2 and 3 is d 2 and d 3 of medium 3 and their dielectric constants are k 2 and k 3 respectively. 6. Conditions for Equilibrium in Various Cases : Suppose three charges q 1 , q 2 and q are situated on a straight line as shown below : If q 1 and q 2 are like charges and q is of unlike charge then, (1) Force on q 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2 1 2 2 1 1 0 1 1 r q r r q 4 q F (2) Force on q 2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2 2 2 2 1 1 0 2 2 r q r r q 4 q F (3) Force on q = ? ? ? ? ? ? ? ? ? ? 2 2 2 2 1 1 0 r q r q 4 1 F Now, from above equations, it is clear that various equilibrium conditions can be as follows : (a) Condition for 1 F to be zero is, ? ? ? ? 2 2 1 2 1 2 2 1 2 2 1 r r r q q r r q r q ? ? ? ? ? (b) Condition for 2 F to be zero is, ? ? ? ? 2 2 1 2 2 1 2 2 1 1 2 2 r r r q q r r q r q ? ? ? ? ? (c) Condition for F to be zero is, 2 2 2 2 1 1 r q r q ? 2 2 2 1 2 1 r r r q ? ? If 2 1 q , q and q are of same type charges in nature, then, (1) Charge q will be in equilibrium, if 0 r q r q 4 q F 2 2 2 2 1 1 0 ? ? ? ? ? ? ? ? ? ? ? 2 1 2 1 1 2 2 2 1 2 2 2 q q q r r r q r ? ? ? ? (2) Charges q 1 and q 2 will not be in equilibrium. Page 4 1 UNIT - 11 ELECTROSTATICS 2 SUMMARY 1. Electric Charge : Just as masses of two particles are responsible for the gravitational force, charges are responsible for the electric force. Electric charge is an intrinsic property of a particle. Charges are of two types : (1) Positive charges (2) Nagative charges. The force acting between two like charges is repulsive and two unlike charges it is attractive between . 2. Quantization of Electric Charge : The magnitude of all charges found in nature are an integral multiple of a fundamental charge. , ne Q ? where e is the fundamental unit of charge. 3. Conservation of Electric Charge : Irrespective of any process taking place, the algebraic sum of electric charges in an electrically isolated system always remains constant. 4. Coulomb's Law : The electric force between two stationary point charges is directly propor- tional to the product of their charges and inversely proportional to the square of the distance between them. 2 2 1 0 2 2 1 r q q 4 1 r q q k F ? ? ? ? If 0 q q 2 1 ? then there is a repulsion between the two charges and for 0 q q 2 2 ? , there is a attrac- tion between the charges. 5. Equation for Force using Columbâ€™s Law, when two charges are placed in a medium having dielectric constant k. (1) The electric force ? ? F experienced by a test charge (q 0 ) due to a source charge (q) when both are placed in a medium having dielectric constant k and separated by a dis- tance r, is given by : r Ë† kr q q 4 1 F 2 2 1 0 ? ? ? F r P O (q) (q o ) Here r Ë† is the unit vector directed from q to q 0 . (2) The equation of coulomb's force may be written as follows : ? ? r Ë† r k q q 4 1 F 2 2 1 0 ? ? ? (3) If the source charge and test charge are separated by a number of medium of thickness 1 2 3 d , d , d ........ having dielectric constants ........ k , k , k 3 2 1 respectively, then the electric force on charge q 0 due to a charge q is given by ? ? 0 2 2 2 0 1 1 2 2 3 3 qq 1 Ë† F r 4 k d k d k d ? ? ? ? ? ? 0 2 0 i i qq 1 Ë† F r 4 k d ? ? ? ? ? ? ? ? OR ? In this equation k i is dielectric constant of medium which spreads through the distance d i along the line joining q and q 0 . 3 For example, see the figure below : Here, the space between the charges q and q 0 is filled with medium (1, 2, 3). The thickness of medium 1 is d 1 and its dielectric consant is k 1 Similarly the thickness of medium 2 and 3 is d 2 and d 3 of medium 3 and their dielectric constants are k 2 and k 3 respectively. 6. Conditions for Equilibrium in Various Cases : Suppose three charges q 1 , q 2 and q are situated on a straight line as shown below : If q 1 and q 2 are like charges and q is of unlike charge then, (1) Force on q 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2 1 2 2 1 1 0 1 1 r q r r q 4 q F (2) Force on q 2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2 2 2 2 1 1 0 2 2 r q r r q 4 q F (3) Force on q = ? ? ? ? ? ? ? ? ? ? 2 2 2 2 1 1 0 r q r q 4 1 F Now, from above equations, it is clear that various equilibrium conditions can be as follows : (a) Condition for 1 F to be zero is, ? ? ? ? 2 2 1 2 1 2 2 1 2 2 1 r r r q q r r q r q ? ? ? ? ? (b) Condition for 2 F to be zero is, ? ? ? ? 2 2 1 2 2 1 2 2 1 1 2 2 r r r q q r r q r q ? ? ? ? ? (c) Condition for F to be zero is, 2 2 2 2 1 1 r q r q ? 2 2 2 1 2 1 r r r q ? ? If 2 1 q , q and q are of same type charges in nature, then, (1) Charge q will be in equilibrium, if 0 r q r q 4 q F 2 2 2 2 1 1 0 ? ? ? ? ? ? ? ? ? ? ? 2 1 2 1 1 2 2 2 1 2 2 2 q q q r r r q r ? ? ? ? (2) Charges q 1 and q 2 will not be in equilibrium. 4 7. Electric Field Intensity : The electric force acting on a unit positive charges at a given point in an electric field of a system of charges is called the electric field or the intensity of electric field ? ? E at that point. q F E ? The SI unit of E is C N or 1 Vm ? . If n 2 1 r ... ,......... r , r are the position vectors of the charges n 2 1 q . ,......... q , q respectively, then the resultant electric field at a point of position vector r is, ? ? j n 1 j 3 j j r r r r q k E ? ? ? ? ? 8. Electric Dipole : A system of two equal and opposite charge, separated by a finite distance is called electric dipole. Electric dipole moment ? ? a 2 q p ? The direction of p is from the negative electric charge to the positive electric charge. 9. Electric field of a dipole on the axis of the dipole at point z = z ? ? ? ? ^ 3 2kp E z p for z a z ? ? ? ? ? Electric field of a dipole on the equator of the dipole at point y = y ? ? ? ? ^ 3 kp E y p for y a y ? ? ? ? ? 10. The torque acting on the dipole place in an uniform the electric field at an angle ? , ? ? ? ? ? ? sin E p | | , E p 11. Electric Flux : Electric flux associated with surface of area A , placed in the uniform electric field. ? ? ? ? ? cos EA A E where, ? is the angle between A and E , Its SI unit is 2 Nm C or V.m. 12. Gauss's Law : The total electric flux associated with the closed surface, 0 S q E d a ? ? ? ? ? ? ? ? ? ? where, q ? is the net charge enclosed by the surface. Page 5 1 UNIT - 11 ELECTROSTATICS 2 SUMMARY 1. Electric Charge : Just as masses of two particles are responsible for the gravitational force, charges are responsible for the electric force. Electric charge is an intrinsic property of a particle. Charges are of two types : (1) Positive charges (2) Nagative charges. The force acting between two like charges is repulsive and two unlike charges it is attractive between . 2. Quantization of Electric Charge : The magnitude of all charges found in nature are an integral multiple of a fundamental charge. , ne Q ? where e is the fundamental unit of charge. 3. Conservation of Electric Charge : Irrespective of any process taking place, the algebraic sum of electric charges in an electrically isolated system always remains constant. 4. Coulomb's Law : The electric force between two stationary point charges is directly propor- tional to the product of their charges and inversely proportional to the square of the distance between them. 2 2 1 0 2 2 1 r q q 4 1 r q q k F ? ? ? ? If 0 q q 2 1 ? then there is a repulsion between the two charges and for 0 q q 2 2 ? , there is a attrac- tion between the charges. 5. Equation for Force using Columbâ€™s Law, when two charges are placed in a medium having dielectric constant k. (1) The electric force ? ? F experienced by a test charge (q 0 ) due to a source charge (q) when both are placed in a medium having dielectric constant k and separated by a dis- tance r, is given by : r Ë† kr q q 4 1 F 2 2 1 0 ? ? ? F r P O (q) (q o ) Here r Ë† is the unit vector directed from q to q 0 . (2) The equation of coulomb's force may be written as follows : ? ? r Ë† r k q q 4 1 F 2 2 1 0 ? ? ? (3) If the source charge and test charge are separated by a number of medium of thickness 1 2 3 d , d , d ........ having dielectric constants ........ k , k , k 3 2 1 respectively, then the electric force on charge q 0 due to a charge q is given by ? ? 0 2 2 2 0 1 1 2 2 3 3 qq 1 Ë† F r 4 k d k d k d ? ? ? ? ? ? 0 2 0 i i qq 1 Ë† F r 4 k d ? ? ? ? ? ? ? ? OR ? In this equation k i is dielectric constant of medium which spreads through the distance d i along the line joining q and q 0 . 3 For example, see the figure below : Here, the space between the charges q and q 0 is filled with medium (1, 2, 3). The thickness of medium 1 is d 1 and its dielectric consant is k 1 Similarly the thickness of medium 2 and 3 is d 2 and d 3 of medium 3 and their dielectric constants are k 2 and k 3 respectively. 6. Conditions for Equilibrium in Various Cases : Suppose three charges q 1 , q 2 and q are situated on a straight line as shown below : If q 1 and q 2 are like charges and q is of unlike charge then, (1) Force on q 1 ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2 1 2 2 1 1 0 1 1 r q r r q 4 q F (2) Force on q 2 ? ? ? ? ? ? ? ? ? ? ? ? ? ? 2 2 2 2 1 1 0 2 2 r q r r q 4 q F (3) Force on q = ? ? ? ? ? ? ? ? ? ? 2 2 2 2 1 1 0 r q r q 4 1 F Now, from above equations, it is clear that various equilibrium conditions can be as follows : (a) Condition for 1 F to be zero is, ? ? ? ? 2 2 1 2 1 2 2 1 2 2 1 r r r q q r r q r q ? ? ? ? ? (b) Condition for 2 F to be zero is, ? ? ? ? 2 2 1 2 2 1 2 2 1 1 2 2 r r r q q r r q r q ? ? ? ? ? (c) Condition for F to be zero is, 2 2 2 2 1 1 r q r q ? 2 2 2 1 2 1 r r r q ? ? If 2 1 q , q and q are of same type charges in nature, then, (1) Charge q will be in equilibrium, if 0 r q r q 4 q F 2 2 2 2 1 1 0 ? ? ? ? ? ? ? ? ? ? ? 2 1 2 1 1 2 2 2 1 2 2 2 q q q r r r q r ? ? ? ? (2) Charges q 1 and q 2 will not be in equilibrium. 4 7. Electric Field Intensity : The electric force acting on a unit positive charges at a given point in an electric field of a system of charges is called the electric field or the intensity of electric field ? ? E at that point. q F E ? The SI unit of E is C N or 1 Vm ? . If n 2 1 r ... ,......... r , r are the position vectors of the charges n 2 1 q . ,......... q , q respectively, then the resultant electric field at a point of position vector r is, ? ? j n 1 j 3 j j r r r r q k E ? ? ? ? ? 8. Electric Dipole : A system of two equal and opposite charge, separated by a finite distance is called electric dipole. Electric dipole moment ? ? a 2 q p ? The direction of p is from the negative electric charge to the positive electric charge. 9. Electric field of a dipole on the axis of the dipole at point z = z ? ? ? ? ^ 3 2kp E z p for z a z ? ? ? ? ? Electric field of a dipole on the equator of the dipole at point y = y ? ? ? ? ^ 3 kp E y p for y a y ? ? ? ? ? 10. The torque acting on the dipole place in an uniform the electric field at an angle ? , ? ? ? ? ? ? sin E p | | , E p 11. Electric Flux : Electric flux associated with surface of area A , placed in the uniform electric field. ? ? ? ? ? cos EA A E where, ? is the angle between A and E , Its SI unit is 2 Nm C or V.m. 12. Gauss's Law : The total electric flux associated with the closed surface, 0 S q E d a ? ? ? ? ? ? ? ? ? ? where, q ? is the net charge enclosed by the surface. 5 13. Electric field due to an infinitely long straight charged wire, , r Ë† r 1 2 E 0 ? ? ? ? where, r is the perpendicular distance from the charged wire. 14. Electric field due to bending of charged rod, 15. Electric field due to uniformly charged thin spherical shell, (1) Electric field inside the shell 0 E ? (2) Electric field at a distance r from the centre outside the shell, 2 2 0 2 r R r q k E ? ? ? ? where, R = radius of spherical shell. 16. Electric field due to a uniformly charged density sphere of radius R, (1) Electric field inside the region of the sphere, 3 0 0 Q r r E 4 R 3 ? ? ? ? ?Read More

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