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Premium member Presentation Transcript PHY-151 : PHY-151 Electricity and Magnetism EM Waves Optics and Optical devices Special theory of Relativity Modern Physics (Atomic Physics) Quantum Mechanics Nuclei and Particles Slide 2: Fig. 15-CO, p. 497 Electricity Mgnetism Chapter 15 : Chapter 15 Electric charge (q) Electric Field (E ) Gauss’s Law E •dS =4pq Ideas From Mechanics : Ideas From Mechanics Concept of Force “F” and concept of mass “m” F=ma Knowledge of F predicts “future” “Charge”A Concept In Electricity and Magnetism E&M : “Charge”A Concept In Electricity and Magnetism E&M Charge Q is the most “fundamental” concept in EM Charge Q What is electric charge? Q : What is electric charge? Q Electric charge is a fundamental physical quantity as fundamental as time and space. Electric charge is a scalar quantity The concept of the Electric charge is used successfully to explain various physical phenomena in E&M. Some properties of charge : Some properties of charge Where are the charges? : Where are the charges? hlektron amber atomoatom Where are the charges? : Where are the charges? Atomic Nuclei carry the positive charges in the form of protons. Each proton has a charge +e The electrons around the atomic nucleus carry the negative charges -e 2H Deuterium atom 6Li Lithium atom 4He Helium atom Proton Charge=+e Neutron Charge=0 Electron Charge=-e Classification of material on their ability to conduct electricity : Classification of material on their ability to conduct electricity Conductors: The charges (electrons) –e are moving freely. Insulators: The charges (electrons) –e do not move freely. Semiconductors: Superconductors: Methods of charging a material : Methods of charging a material Conduction Induction Some Evidence on the Existence of Charges : Some Evidence on the Existence of Charges Charging a material by “Conduction” Silk & Glass Fur & Rubber rod Negative charges (electrons) – e Move to Silk Move to Rubber rod from the Fur Experiment: : Experiment: Show that the assumption of two kind of Electric charges is compatible with the experimental observations Charging by Conduction : Charging by Conduction a) A charged object (the rod) is close to another object (the sphere) b) A charged object (the rod) is placed in contact with another object (the sphere) Some electrons on the rod can move to the sphere c) When the rod is removed, the sphere is left with a charge The object being charged is always left with a charge having the same sign as the object doing the charging Charging an object by Inductionform a distance : When an object is connected to a conducting wire or pipe buried in the earth, it is said to be grounded A neutral sphere has equal number of electrons and protons Charging an object by Inductionform a distance a) A charged object (the rod) is close to another object (the sphere) b) The electrons in the sphere move away from the rod. High concentration of electron opposite to rod c) Connect a wire from the ground to the sphere Electrons will move from the sphere to the ground Disconnect wire When rod is removed the sphere remains charged Polarization : Polarization A molecule has electric polarization ( p ) if the center of positive charge +Q is different from the center of the negative charge -Q d p Electric dipole moment p p=Qd Q is the Charge d is the distance of +Q and -Q + - + - Polarization : Polarization In most (not all) neutral atoms or molecules, the center of positive charge coincides with the center of negative charge. In the presence of a charged object, these centers may separate slightly This results in more positive charge on one side of the molecule than on the other side. This realignment of charge on the surface of an insulator is known as polarization Examples of Electrical Polarization : The charged object (on the left) induces charge on the surface of the insulator A charged comb attracts bits of paper due to polarization of the paper Examples of Electrical Polarization Evidence of the electrical polarization of H2O molecules : Evidence of the electrical polarization of H2O molecules Explain; : Explain; H2O molecules attracted by the Rubber rod “curve” Coulomb’s Law: “Start being quantitative” : Coulomb’s Law: “Start being quantitative” ke is called the Coulomb Constant ke = 8.9875 x 109 N m2/C2 q1 and q2 in Coulombs r in [m] The Law as it appears in Equation (1) applies only to point charges Describes the interaction between point charges (1) Coulomb’s Law: : Coulomb’s Law: What if many point charges are present? q2 q1 q3 q4 q5 F15=k(q1q5)/r152 F14=k(q1q4)/r142 F13=k(q1q3)/r132 F12=k(q1q2)/r122 Fnet=F12+F13+F14+F15 The Superposition Principle : The Superposition Principle The resultant force on any one charge equals the vector sum of the forces exerted by the other individual charges that are present Find the electrical forces between pairs of charges separately Then add the vectors Apply the vector rules when adding vectors Fnet=F12+F13+F14+F15 Example 1 : Example 1 The Hydrogen atom consists of: A protons of mass mp=1.67x10-27 kg and charge qp= 1.6x10-19 C and an electron of mass me=9.11x10-31 kg and charge qe=-1.6x10-19 C. The electron revolves around the proton on a circular orbit of radius R=5.3x10-11 m. Calculate: a) the speed v of the electron and b) the frequency f of revolution Method A: v={(6.67x10-11)(1.67x10-27)/(5.3x10-11) +(8.99x109)(1.6x10-19)2/[(5.3x10-11) (9.11x10-31)}1/2 m/s=2.183x106 m/s a) f= 2.183x106/(2x3.14x5.3x10-11 ) Hz=6.55x1015 b) Example 1 : Example 1 The Hydrogen atom consists of: A protons of mass mp=1.67x10-27 kg and charge qp= 1.6x10-19 C and an electron of mass me=9.11x10-31 kg and charge qe=-1.6x10-19 C. The electron revolves around the proton on a circular orbit of radius R=5.3x10-11 m. Calculate: a) the speed v of the electron and b) the frequency f of revolution Method A: v={(6.67x10-11)(1.67x10-27)/(5.3x10-11) +(8.99x109)(1.6x10-19)2/[(5.3x10-11) (9.11x10-31)}1/2 m/s=2.183x106 m/s a) f= 2.183x106/(2x3.14x5.3x10-11 ) Hz=6.55x1015 b) Grade 0 Example 1 : Example 1 The Hydrogen atom consists of: A protons of mass mp=1.67x10-27 kg and charge qp= 1.6x10-19 C and an electron of mass me=9.11x10-31 kg and charge qe=-1.6x10-19 C. The electron revolves around the proton on a circular orbit of radius R=5.3x10-11 m. {ke=8.99x109 (Nm2/C2), G=6.67x10-11 (Nm2/Kg2)} Calculate: a) the speed v of the electron and b) the frequency f of revolution Fcentral=Fgrav+Fcoulomb=G(mpme)/R2+ke(qpqe)/R2 (1) Fcentral=(mev2)/R (2) (mev2)/R =G(mpme)/R2+ke(qpqe)/R2 b) f=v/(2pR) Calculate numerical value of f=…. Hz v={G(mp)/R + ke(qpqe)/(meR)}1/2 Calculate numerical value of v=…. m/s Example 15.2 textbook : Example 15.2 textbook L= a) Find x, for the Resultant Force on q3 to be Zero. q1=15 mC , q2=6 mC , q3<0. b) What if q3 is positive? FR=F23+F13 =-|F23|+|F13| =-ke(q2q3)/x2+ke(q1q3)/(L-x)2=0 => -q2/x2+q1/(L-x)2=0 => -q2(L-x)2+q1x2=(q1-q2)x2 +2Lq2x-q2L=0 (q1-q2)x2 +2Lq2x-q2L2=0 9x2 +24x-24=0=> 3x2 +8x-8=0 Superposition Principle Example : Superposition Principle Example The force exerted by q1 on q3 is F13 The force exerted by q2 on q3 is F23 The total force exerted on q3 is the vector sum F13 and F23 R13= R23= Superposition Principle Example : Superposition Principle Example R13= R23= F13=ke(q1q3)/R132 angle =q13 F23=ke(q2q3)/R232 angle =q23 R13=5 m, q13=37o R23=4 m, q23=180o Fresultant=(Fx2+ Fy2)1/2 q = tan-1(Fy/Fx) ke=8.9875x109 Nm2/C2 q1= 1mC, q2=-2 mC, q3=0.3 mC Electric Field E generated by a charge Q : Electric Field E generated by a charge Q F=(keQ)q0/r2 (radial direction) SI units are N / C E E q0 + Electric Field for Negative charge -Q : Electric Field for Negative charge -Q F=(keQ)q0/r2 (radial direction) SI units are N / C The electric field produced by a negative charge is directed toward the charge E Q +q0 +q0 Summary : Summary +q0 +q0 -Q +Q Why do we need E field? is’nt F (Force) enough? : Why do we need E field? is’nt F (Force) enough? E field at a point is independent of the test charge and depends on the charge distribution itself. E field (electric field), along with B field (magnetic field), are both used in a set of very important equations, ”Maxwell’s equation” which govern the field of Electricity and Magnetism. R x y E F Electric Field Lines of point +q, -q charges : Electric Field Lines of point +q, -q charges For a point q the E Field_lines same the E_field E E Electric Field Lines of an Electric dipole : Electric Field Lines of an Electric dipole Calculate the ER : ER is tangent to the E_Field lines E E Electric Field Lines : Electric Field Lines The field lines are related to the E field in the following manners: The electric field vector, E , is tangent to the electric field lines at each point. The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region Electric Field Lines : Electric Field Lines Given the charge distribution we can mathematically derive the functions f(x,y) which provides the electric field lines. Show of E_field Lines : Show of E_field Lines http://qbx6.ltu.edu/s_schneider/physlets/main/efield.shtml http://www.cco.caltech.edu/~phys1/java/phys1/EField/EField.html What is the need of the electric Field Lines? : What is the need of the electric Field Lines? A convenient aid for visualizing electric field patterns is to draw lines pointing in the direction of the field vector at any point. Show where the field is intense. Help determine the E_field on systems which exhibit symmetry. Conductors in Electrostatic Equilibrium : Conductors in Electrostatic Equilibrium When no net motion of charge occurs within a conductor, the conductor is said to be in electrostatic equilibrium An isolated conductor has the following properties: The electric field is zero everywhere inside the conducting material Any excess charge on an isolated conductor resides entirely on its surface The electric field just outside a charged conductor is perpendicular to the conductor’s surface E E=0 Conductor Electric Charge Electric Flux F : Electric Flux F Field lines penetrating an area A perpendicular to the field The product of E•A is the flux, F F is a scalar quantity. In general: ΦE = E A cos θ Gauss’ Law : Gauss’ Law Gauss’ Law states that the electric FF flux through any closed surface is equal to the net charge Qinside the surface divided by εo εo permittivity of free space εo=8.8542 x 10-12 C2/Nm2 The area in Φ is an imaginary surface, which encloses the charge Qinside S(Ei Ai cos θ)= Ei θ Ai Consequence of….. E=(ke)(Q/r2) Electric Field of a Charged (Q) Thin Conducting Spherical Shell : Electric Field of a Charged (Q) Thin Conducting Spherical Shell Calculate the E field at any point on a sphere of radius r b) Invoke symmetry to establish direction of E a) The charge is uniformly distributed on the shell c) Symmetry to establish strength of Ei at radius r Use Gauss’s Law: S(Ei Ai cos θ)=Q/e0 Ei and Ai collinear =>q=0 Q/e0=S(Ei Ai)=EiS(Ai)= Ei 4pr2 Eoutside=(1/4pe0)(Q/r2) Same as central charge x x Electric Field of a Nonconducting Infinite Plane Sheet Charged Uniformly : Electric Field of a Nonconducting Infinite Plane Sheet Charged Uniformly a) The charge is uniformly distributed on the sheet b) Invoke symmetry to establish direction of E Surface Charge density s=Q/A0 c) Symmetry to establish strength of E |Eup|= |Edown|= E Eup Edown x x E=s/(2e0) Use Gauss’s Law on the cylindrical surface: S(Ei Ai cos θ)=Q/e0 => (EupAi+EdownAi +EsideAside)=Q/e0 2EA=Q/e0 => E=Q/(2Ae0) =s/(2e0) Electric Field of a Nonconducting Infinite Plane Sheet Charged Uniformly : Electric Field of a Nonconducting Infinite Plane Sheet Charged Uniformly Surface Charge density s=Q/A0 Eup Edown E=s/(2e0) Use Gauss’s Law on the cylindrical surface: S(Ei Ai cos θ)=Q/e0 => (EupAi+EdownAi +EsideAside)=Q/e0 2EA=Q/e0 => E=Q/(2Ae0) =s/(2e0) Eup Edown E field of a Parallel Plate Capacitor : E field of a Parallel Plate Capacitor Infinite plates Charge Uniformly Uniformly distributed s Problem: E field of a Parallel Plate Capacitor : Problem: E field of a Parallel Plate Capacitor A very large non-conducting plate Charge Uniformly Uniformly distributed s Experiments to Verify Properties of Charges : Experiments to Verify Properties of Charges Faraday’s Ice-Pail Experiment Conclusions: An induced charge has the same magnitude as the inducing charge. The charge on a conductor remains on the outside surface; there can be no net charge inside a hollow conductor (either there are equal quantities of opposite charge or there in no charge) Experiments to Verify Properties of Charges : Experiments to Verify Properties of Charges Millikan Oil-Drop Experiment Measured the elementary charge, e Quantization of charge Q = n e Van de Graaff GeneratorAccelerates ions : Van de Graaff GeneratorAccelerates ions An electrostatic generator designed and built by Robert J. Van de Graaff in 1929 Charge is transferred to the dome by means of a rotating belt Positive ions in the dome are accelerated when reach ground potential. You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
Lecture of Chapter 15 ntsoupas Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 449 Category: Education License: All Rights Reserved Like it (0) Dislike it (0) Added: January 25, 2010 This Presentation is Public Favorites: 0 Presentation Description ppt file Comments Posting comment... Premium member Presentation Transcript PHY-151 : PHY-151 Electricity and Magnetism EM Waves Optics and Optical devices Special theory of Relativity Modern Physics (Atomic Physics) Quantum Mechanics Nuclei and Particles Slide 2: Fig. 15-CO, p. 497 Electricity Mgnetism Chapter 15 : Chapter 15 Electric charge (q) Electric Field (E ) Gauss’s Law E •dS =4pq Ideas From Mechanics : Ideas From Mechanics Concept of Force “F” and concept of mass “m” F=ma Knowledge of F predicts “future” “Charge”A Concept In Electricity and Magnetism E&M : “Charge”A Concept In Electricity and Magnetism E&M Charge Q is the most “fundamental” concept in EM Charge Q What is electric charge? Q : What is electric charge? Q Electric charge is a fundamental physical quantity as fundamental as time and space. Electric charge is a scalar quantity The concept of the Electric charge is used successfully to explain various physical phenomena in E&M. Some properties of charge : Some properties of charge Where are the charges? : Where are the charges? hlektron amber atomoatom Where are the charges? : Where are the charges? Atomic Nuclei carry the positive charges in the form of protons. Each proton has a charge +e The electrons around the atomic nucleus carry the negative charges -e 2H Deuterium atom 6Li Lithium atom 4He Helium atom Proton Charge=+e Neutron Charge=0 Electron Charge=-e Classification of material on their ability to conduct electricity : Classification of material on their ability to conduct electricity Conductors: The charges (electrons) –e are moving freely. Insulators: The charges (electrons) –e do not move freely. Semiconductors: Superconductors: Methods of charging a material : Methods of charging a material Conduction Induction Some Evidence on the Existence of Charges : Some Evidence on the Existence of Charges Charging a material by “Conduction” Silk & Glass Fur & Rubber rod Negative charges (electrons) – e Move to Silk Move to Rubber rod from the Fur Experiment: : Experiment: Show that the assumption of two kind of Electric charges is compatible with the experimental observations Charging by Conduction : Charging by Conduction a) A charged object (the rod) is close to another object (the sphere) b) A charged object (the rod) is placed in contact with another object (the sphere) Some electrons on the rod can move to the sphere c) When the rod is removed, the sphere is left with a charge The object being charged is always left with a charge having the same sign as the object doing the charging Charging an object by Inductionform a distance : When an object is connected to a conducting wire or pipe buried in the earth, it is said to be grounded A neutral sphere has equal number of electrons and protons Charging an object by Inductionform a distance a) A charged object (the rod) is close to another object (the sphere) b) The electrons in the sphere move away from the rod. High concentration of electron opposite to rod c) Connect a wire from the ground to the sphere Electrons will move from the sphere to the ground Disconnect wire When rod is removed the sphere remains charged Polarization : Polarization A molecule has electric polarization ( p ) if the center of positive charge +Q is different from the center of the negative charge -Q d p Electric dipole moment p p=Qd Q is the Charge d is the distance of +Q and -Q + - + - Polarization : Polarization In most (not all) neutral atoms or molecules, the center of positive charge coincides with the center of negative charge. In the presence of a charged object, these centers may separate slightly This results in more positive charge on one side of the molecule than on the other side. This realignment of charge on the surface of an insulator is known as polarization Examples of Electrical Polarization : The charged object (on the left) induces charge on the surface of the insulator A charged comb attracts bits of paper due to polarization of the paper Examples of Electrical Polarization Evidence of the electrical polarization of H2O molecules : Evidence of the electrical polarization of H2O molecules Explain; : Explain; H2O molecules attracted by the Rubber rod “curve” Coulomb’s Law: “Start being quantitative” : Coulomb’s Law: “Start being quantitative” ke is called the Coulomb Constant ke = 8.9875 x 109 N m2/C2 q1 and q2 in Coulombs r in [m] The Law as it appears in Equation (1) applies only to point charges Describes the interaction between point charges (1) Coulomb’s Law: : Coulomb’s Law: What if many point charges are present? q2 q1 q3 q4 q5 F15=k(q1q5)/r152 F14=k(q1q4)/r142 F13=k(q1q3)/r132 F12=k(q1q2)/r122 Fnet=F12+F13+F14+F15 The Superposition Principle : The Superposition Principle The resultant force on any one charge equals the vector sum of the forces exerted by the other individual charges that are present Find the electrical forces between pairs of charges separately Then add the vectors Apply the vector rules when adding vectors Fnet=F12+F13+F14+F15 Example 1 : Example 1 The Hydrogen atom consists of: A protons of mass mp=1.67x10-27 kg and charge qp= 1.6x10-19 C and an electron of mass me=9.11x10-31 kg and charge qe=-1.6x10-19 C. The electron revolves around the proton on a circular orbit of radius R=5.3x10-11 m. Calculate: a) the speed v of the electron and b) the frequency f of revolution Method A: v={(6.67x10-11)(1.67x10-27)/(5.3x10-11) +(8.99x109)(1.6x10-19)2/[(5.3x10-11) (9.11x10-31)}1/2 m/s=2.183x106 m/s a) f= 2.183x106/(2x3.14x5.3x10-11 ) Hz=6.55x1015 b) Example 1 : Example 1 The Hydrogen atom consists of: A protons of mass mp=1.67x10-27 kg and charge qp= 1.6x10-19 C and an electron of mass me=9.11x10-31 kg and charge qe=-1.6x10-19 C. The electron revolves around the proton on a circular orbit of radius R=5.3x10-11 m. Calculate: a) the speed v of the electron and b) the frequency f of revolution Method A: v={(6.67x10-11)(1.67x10-27)/(5.3x10-11) +(8.99x109)(1.6x10-19)2/[(5.3x10-11) (9.11x10-31)}1/2 m/s=2.183x106 m/s a) f= 2.183x106/(2x3.14x5.3x10-11 ) Hz=6.55x1015 b) Grade 0 Example 1 : Example 1 The Hydrogen atom consists of: A protons of mass mp=1.67x10-27 kg and charge qp= 1.6x10-19 C and an electron of mass me=9.11x10-31 kg and charge qe=-1.6x10-19 C. The electron revolves around the proton on a circular orbit of radius R=5.3x10-11 m. {ke=8.99x109 (Nm2/C2), G=6.67x10-11 (Nm2/Kg2)} Calculate: a) the speed v of the electron and b) the frequency f of revolution Fcentral=Fgrav+Fcoulomb=G(mpme)/R2+ke(qpqe)/R2 (1) Fcentral=(mev2)/R (2) (mev2)/R =G(mpme)/R2+ke(qpqe)/R2 b) f=v/(2pR) Calculate numerical value of f=…. Hz v={G(mp)/R + ke(qpqe)/(meR)}1/2 Calculate numerical value of v=…. m/s Example 15.2 textbook : Example 15.2 textbook L= a) Find x, for the Resultant Force on q3 to be Zero. q1=15 mC , q2=6 mC , q3<0. b) What if q3 is positive? FR=F23+F13 =-|F23|+|F13| =-ke(q2q3)/x2+ke(q1q3)/(L-x)2=0 => -q2/x2+q1/(L-x)2=0 => -q2(L-x)2+q1x2=(q1-q2)x2 +2Lq2x-q2L=0 (q1-q2)x2 +2Lq2x-q2L2=0 9x2 +24x-24=0=> 3x2 +8x-8=0 Superposition Principle Example : Superposition Principle Example The force exerted by q1 on q3 is F13 The force exerted by q2 on q3 is F23 The total force exerted on q3 is the vector sum F13 and F23 R13= R23= Superposition Principle Example : Superposition Principle Example R13= R23= F13=ke(q1q3)/R132 angle =q13 F23=ke(q2q3)/R232 angle =q23 R13=5 m, q13=37o R23=4 m, q23=180o Fresultant=(Fx2+ Fy2)1/2 q = tan-1(Fy/Fx) ke=8.9875x109 Nm2/C2 q1= 1mC, q2=-2 mC, q3=0.3 mC Electric Field E generated by a charge Q : Electric Field E generated by a charge Q F=(keQ)q0/r2 (radial direction) SI units are N / C E E q0 + Electric Field for Negative charge -Q : Electric Field for Negative charge -Q F=(keQ)q0/r2 (radial direction) SI units are N / C The electric field produced by a negative charge is directed toward the charge E Q +q0 +q0 Summary : Summary +q0 +q0 -Q +Q Why do we need E field? is’nt F (Force) enough? : Why do we need E field? is’nt F (Force) enough? E field at a point is independent of the test charge and depends on the charge distribution itself. E field (electric field), along with B field (magnetic field), are both used in a set of very important equations, ”Maxwell’s equation” which govern the field of Electricity and Magnetism. R x y E F Electric Field Lines of point +q, -q charges : Electric Field Lines of point +q, -q charges For a point q the E Field_lines same the E_field E E Electric Field Lines of an Electric dipole : Electric Field Lines of an Electric dipole Calculate the ER : ER is tangent to the E_Field lines E E Electric Field Lines : Electric Field Lines The field lines are related to the E field in the following manners: The electric field vector, E , is tangent to the electric field lines at each point. The number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region Electric Field Lines : Electric Field Lines Given the charge distribution we can mathematically derive the functions f(x,y) which provides the electric field lines. Show of E_field Lines : Show of E_field Lines http://qbx6.ltu.edu/s_schneider/physlets/main/efield.shtml http://www.cco.caltech.edu/~phys1/java/phys1/EField/EField.html What is the need of the electric Field Lines? : What is the need of the electric Field Lines? A convenient aid for visualizing electric field patterns is to draw lines pointing in the direction of the field vector at any point. Show where the field is intense. Help determine the E_field on systems which exhibit symmetry. Conductors in Electrostatic Equilibrium : Conductors in Electrostatic Equilibrium When no net motion of charge occurs within a conductor, the conductor is said to be in electrostatic equilibrium An isolated conductor has the following properties: The electric field is zero everywhere inside the conducting material Any excess charge on an isolated conductor resides entirely on its surface The electric field just outside a charged conductor is perpendicular to the conductor’s surface E E=0 Conductor Electric Charge Electric Flux F : Electric Flux F Field lines penetrating an area A perpendicular to the field The product of E•A is the flux, F F is a scalar quantity. In general: ΦE = E A cos θ Gauss’ Law : Gauss’ Law Gauss’ Law states that the electric FF flux through any closed surface is equal to the net charge Qinside the surface divided by εo εo permittivity of free space εo=8.8542 x 10-12 C2/Nm2 The area in Φ is an imaginary surface, which encloses the charge Qinside S(Ei Ai cos θ)= Ei θ Ai Consequence of….. E=(ke)(Q/r2) Electric Field of a Charged (Q) Thin Conducting Spherical Shell : Electric Field of a Charged (Q) Thin Conducting Spherical Shell Calculate the E field at any point on a sphere of radius r b) Invoke symmetry to establish direction of E a) The charge is uniformly distributed on the shell c) Symmetry to establish strength of Ei at radius r Use Gauss’s Law: S(Ei Ai cos θ)=Q/e0 Ei and Ai collinear =>q=0 Q/e0=S(Ei Ai)=EiS(Ai)= Ei 4pr2 Eoutside=(1/4pe0)(Q/r2) Same as central charge x x Electric Field of a Nonconducting Infinite Plane Sheet Charged Uniformly : Electric Field of a Nonconducting Infinite Plane Sheet Charged Uniformly a) The charge is uniformly distributed on the sheet b) Invoke symmetry to establish direction of E Surface Charge density s=Q/A0 c) Symmetry to establish strength of E |Eup|= |Edown|= E Eup Edown x x E=s/(2e0) Use Gauss’s Law on the cylindrical surface: S(Ei Ai cos θ)=Q/e0 => (EupAi+EdownAi +EsideAside)=Q/e0 2EA=Q/e0 => E=Q/(2Ae0) =s/(2e0) Electric Field of a Nonconducting Infinite Plane Sheet Charged Uniformly : Electric Field of a Nonconducting Infinite Plane Sheet Charged Uniformly Surface Charge density s=Q/A0 Eup Edown E=s/(2e0) Use Gauss’s Law on the cylindrical surface: S(Ei Ai cos θ)=Q/e0 => (EupAi+EdownAi +EsideAside)=Q/e0 2EA=Q/e0 => E=Q/(2Ae0) =s/(2e0) Eup Edown E field of a Parallel Plate Capacitor : E field of a Parallel Plate Capacitor Infinite plates Charge Uniformly Uniformly distributed s Problem: E field of a Parallel Plate Capacitor : Problem: E field of a Parallel Plate Capacitor A very large non-conducting plate Charge Uniformly Uniformly distributed s Experiments to Verify Properties of Charges : Experiments to Verify Properties of Charges Faraday’s Ice-Pail Experiment Conclusions: An induced charge has the same magnitude as the inducing charge. The charge on a conductor remains on the outside surface; there can be no net charge inside a hollow conductor (either there are equal quantities of opposite charge or there in no charge) Experiments to Verify Properties of Charges : Experiments to Verify Properties of Charges Millikan Oil-Drop Experiment Measured the elementary charge, e Quantization of charge Q = n e Van de Graaff GeneratorAccelerates ions : Van de Graaff GeneratorAccelerates ions An electrostatic generator designed and built by Robert J. Van de Graaff in 1929 Charge is transferred to the dome by means of a rotating belt Positive ions in the dome are accelerated when reach ground potential.