September 9. Physics 272. Fall Prof. Philip von Doetinchem

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1 Physics 272 September 9 Fall Prof. Philip von Doetinchem philipvd@hawaii.edu Phys272 - Fall 14 - von Doetinchem - 120

2 Summary Electric dipole in an external field Phys272 - Fall 14 - von Doetinchem - 121

3 Potential energy of an electric dipole =0: pot. energy minimal, stable equilibrium, dipole parallel to field = /2: pot. energy 0, dipole perpendicular to field = pot. energy maximum, dipole antiparallel to field Electric-field torque does work on dipole change in potential energy Dipoles try to minimize potential energy An uncharged object with a dipole moment can experience a net force in a non-uniform electric field (polarization can happen due to electric field) Phys272 - Fall 14 - von Doetinchem - 122

4 Electric flux and enclosed charge If there is no enclosed charged: electric field flux going into the surface cancels flux out of the surface. Charges outside the enclosed surface do not give a net electric flux. Phys272 - Fall 14 - von Doetinchem - 125

5 Flux of an uniform electric field Phys272 - Fall 14 - von Doetinchem - 126

6 Flux of a nonuniform field General definition of electric flux: If flux is not uniform and area is curved just integrate over infinitesimal area elements d General electric flux definition Phys272 - Fall 14 - von Doetinchem - 127

7 Electric flux through a sphere Surface is not flat, electric field not uniform make smart choice on enclosing surface to simplify the problem, make use of symmetries Electric field is perpendicular to surface Radius cancels out the flux through any surface enclosing a single point charge is independent of the shape or size of the surface Phys272 - Fall 14 - von Doetinchem - 128

8 Gauß's law is an alternative to Coulomb's law and is a different way to express the relationship between electric charge and electric field. Source: Gauß's law Carl Friedrich Gauß ( ) Electric flux is independent of exact radius and only depends on enclosed charge. If you increase the size of the sphere, the electric field gets smaller, but the area increases electric flux stays constant Phys272 - Fall 14 - von Doetinchem - 129

9 Point charge inside a nonspherical surface Electric flux is positive (negative) where the electric field points out (into) of the surface Electric field lines can begin or end inside a region of space only when there is charge in that region Phys272 - Fall 14 - von Doetinchem - 130

10 General form of Gauß's law Surface encloses multiple charges Total electric field is the vector sum of the electric fields of the individual charges General form: The total electric flux through a closed surface is equal to the total (net) electric charge inside the surface, divided by 0. Phys272 - Fall 14 - von Doetinchem - 131

11 Faraday's icepail experiment Phys272 - Fall 14 - von Doetinchem - 132

12 Faraday's icepail experiment Rod inside pail: Position of rod does not matter: reading of electroscope does not change Charge on inside wall opposite of outside wall Charge of pail is the same as the rod Take rod out: electroscope reads zero remove electrons on surface (e.g., by touching) remove rod Conducting ball touches pail: Charge transfers to surface of pail Take ball out: no charge on ball, but charge on pail surface Phys272 - Fall 14 - von Doetinchem - 133

13 Applications of Gauß's Law If charge distribution is known and has enough symmetry the integral can be evaluated If we know the field we can find the charge distribution. Typical question: what is the electric field caused by a charge distribution on a conductor. Excess charge at rest on a solid conductor resides entirely on the surface, and not in the interior. Phys272 - Fall 14 - von Doetinchem - 136

14 Field of a charged conducting sphere surface integral apply Gauss' law Field inside is zero in a conductor Field outside is the same as for a point charge Phys272 - Fall 14 - von Doetinchem - 137

15 Field of a charged insulating sphere apply Gauss' law surface integral Electric field is a continuous function of the radius (in contrast to conductor) Phys272 - Fall 14 - von Doetinchem - 138

16 Faraday cage Phys272 - Fall 14 - von Doetinchem - 139

17 Faraday cage Faraday cages protect against the external influence of electric fields All charges in a conductor reside on the outer surface, and always rearrange themselves to cancel out the electric field in the interior. Vacuum chamber: Electric noise from pumps distorts measurement Sensitive silicon detector Phys272 - Fall 14 - von Doetinchem - 140

18 Electric potential energy Charged particle moving in a field: field exerts work on particle Work can be expressed as potential energy: position of a charge in an electric field Use electric potential to describe potential electric energy potential differences are important for understanding of electric circuits Work done on a particle to move from a to b: change of potential energy for a conservative force (reversible): Phys272 - Fall 14 - von Doetinchem - 142

19 Electric potential energy in an uniform field a d b Conservative force independent of exact path Potential energy decreases if a charged particle moves in the direction of the electric field If the displacement of a positive charge is in the direction of the electric field the work is positive Phys272 - Fall 14 - von Doetinchem - 143

20 Electric potential energy of two point charges Potential energy of two point charges Potential energy defined to some reference point Shared property of both charges Electric field is the vector sum and the total potential energy is the algebraic sum (potential energy is NOT a vector): Phys272 - Fall 14 - von Doetinchem - 144

21 Electric potential Describe potential energy on a per unit charge basis (like the electric field describes force per unit charge) Determination of electric field is often easier by using the potential Source: Alessandro Volta Potential energy and potential are scalars Potential difference in circuits is often called voltage Phys272 - Fall 14 - von Doetinchem - 146

Chapter 18. Electric Forces and Electric Fields

Chapter 18. Electric Forces and Electric Fields My lecture slides may be found on my website at http://www.physics.ohio-state.edu/~humanic/ ------------------------------------------------------------------- Chapter 18 Electric Forces and Electric Fields