Review Exam 1 Electricity and Magnetism Scalar Field A function that gives us a single value of some variable for every point in space Example temperature variation atmospheric pressure Vector Field A quantity that has both a magnitude and a direction in space Example uid ow velocity momentum acceleration force gravity Gravitational Force Electric charge can either be negative or positive Charge of an electron e 1 602 10 19 Charge is quantized Ne Charge is conserved it can neither be created nor destroyed You can get charged via friction transfer touching induction Coulomb s Law Force on q2 due to the interaction between q1 and q2 Superposition Principle Net force on any charge is the vector sum of forces from other individual charges Electric Field at point P Electric eld lines Direction of eld at any point is tangent to eld line at that point Field lines point away from positive charges and terminate on negative charges Field lines never cross each other Force on a charged object with charge q at a point P in an electric eld E due to a source is F P qE P Group Problem Coulomb s Law Vector Analysis Find a vector expression for the unit vectors in terms of and j Force on a Charged Object Three charged objects are located at the positions shown in the gure Find a vector expression for the force on the negatively charged object at P r r r F F F Electric Field on Axis Symmetry Consider two point charges of equal magnitude but opposite signs separated by a distance d Point P lies along the perpendicular bisector of the line joining the charges a distance s above that line What is the E eld at P Concept Questions Five Equal Charges Six equal positive charges q sit at the vertices of a regular hexagon with sides of length R We remove the bottom charge The electric eld at the center of the hexagon point P is Field Lines Electric eld lines show Directions of forces that exist in space at all times Directions in which positive charges on those lines will accelerate Paths that charges will follow More than one of the above Electric Field Two charged objects are placed on a line as shown below The magnitude of the negative charge on the right is greater than the magnitude of the positive charge on the left qR qL Other than at in nity where is the electric eld zero Between the two charged objects To the right of the charged object on the right To the left of the charged object on the left The electric eld is nowhere zero Gauss s Law Dipole in Uniform Field p 2qa cos sin j Torque on dipole r x F p x E rF sin 2a qE sin pEsin Volume V R L Q V Q V uniform Area A wL Q A Q A uniform Length L Q L Q L uniform The rst Maxwell Equation E A Qenclosed For closed surface A is normal to the surface and point outward For electric eld that has constant magnitude on surface Case One if electric eld points out then EA Case Two if electric eld points out then EA Case Three E not uniform surface curved For closed surface A is normal to surface and points outward 0 if E points out 0 if E points in E A Qenclosed V Electric ux through any arbitrary closed surface is proportional to the charge enclosed inside that closed surface Group Problems Gauss s Law holds for all closed surfaces However it is only useful to calculate electric eld for sources with enough of symmetry in which there exists closed surfaces such that The electric eld on some faces of the closed surface is both perpendicular to the face and has constant magnitude on that face then E A EA The electric eld on some faces of the closed surface is parallel to that face Then E A 0 Sphere Consider a point like charged object with charge Q located at the origin What is the electric ux on a spherical surface Gaussian surface of radius r Spherical Symmetry Q uniformly distributed throughout non conducting solid sphere of radius a Determine the direction and magnitude of the electric eld inside the sphere r a Planar Symmetry Consider an in nite thin slab with uniform positive charge density Find a vector expression for the direction and magnitude of the electric eld outside the slab Make sure you know your Gaussian closed surface Cylindrical Symmetry An in nitely long rod has a uniform positive linear charge density Find the direction and magnitude of the electric eld outside the rod Concept Questions Dipole Field As you move to large distances r away from a dipole the electric eld will fall off as 1 r2 just like a point charge More rapidly than 1 r2 More slowly than 1 r2 Dipole in Non Uniform Field Due to the electric eld this dipole will feel force but no torque no force but a torque both a force and a torque neither a force nor a torque Electric Field of a Uniformly Charged Ring A uniformly charged ring of radius a has total charge Q Which of the following expressions best describes the electric eld at the point P located at the center of the ring Scaling and Electric Fields You are told that the electric eld for a source of charges falls like 1 r far away from the source Which of the following sources could produce such an electric eld Dipole Point charge Line of charge Plane of charge Flux thru Sphere The total ux through the below spherical surface is positive net outward ux negative net inward ux zero Sign of Flux The electric ux through the planar surface below positive unit normal to left is positive negative zero Positive Negative Zero Zero Gauss s Law The grass seeds gure shows the electric eld of three charges with charges 1 1 and 1 The Gaussian surface in the gure is a sphere containing two of the charges The electric ux through the spherical Gaussian surface is Spherical Shell We just saw that in a solid sphere of charge the electric eld grows linearly with distance Inside the charged a spherical shell at right r a what does the electric eld do Uniform but Non Zero Still grows linearly Some other functional form use Gauss Law Can t determine with Gauss Law Superposition Three in nite sheets of charge are shown above The sheet in the middle is negatively charged with charge per unit area 2 and the other two sheets are positively charged with charge per unit area Which set of arrows and zeros best describes the electric eld Faraday s Law Electric current I Q t Magnetic eld of bar magnet magnetic eld lines leave from the north pole and end at the south pole Flux is the generalization of ow B A Electromotive Force emf F q s If the closed path is a circuit with resistance R then the electromotive force will cause a current to …
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