ElectricFieldsHongKongPolytechnicUniversityExample:Thefigure shows threeparticles withchargesi=+2Q,q2=-2Q,and q3=-4Q,eacha distancedfromtheorigin.WhatnetelectricfieldEisproducedattheorigin?Solution:3093080Example: The nucleus of a uranium atomhas aradius R of 6.8 fm.Assuming that thepositive charge of the nucleus is distributed uniformly, determine the electric field at a pointonthesurfaceofthenucleusduetothatcharge.Solution:TheatomicnumberZ-92
Hong Kong Polytechnic University Electric Fields Example: The figure shows three particles with charges q1=+2Q, q2=2Q, and q3=4Q, each a distance d from the origin. What net electric field E is produced at the origin? Solution: Example: The nucleus of a uranium atom has a radius R of 6.8 fm. Assuming that the positive charge of the nucleus is distributed uniformly, determine the electric field at a point on the surface of the nucleus due to that charge. Solution: The atomic number Z=92
ElectricFieldsHongKongPolytechnicUniversityElectricFieldLines（电力线）：Electricfieldlinesprovideameansforvisualizingthedirectionandmagnitudeofelectric fields.The electric field vector at any point is tangent to a field line throughthat point. The density of field lines in any region is proportional to the magnitude ofthe electric fieldinthatregion.Field lines originate on positivecharges andterminateonnegativecharges.Afewexamplesareshownbelow:ElectricfieldlineElectricDipole（电偶极子）Field:Anelectricdipoleconsistsoftwoparticleswithchargesofequalmagnitudegbutopposite sign, separated byasmall distance d.It canbeprovedthattheelectricfieldgeneratedbythedipolealongthedipoleaxisiswhereristhedistancetothecenterofthedipoler>>d
Hong Kong Polytechnic University Electric Fields Electric Field Lines (电力线): Electric field lines provide a means for visualizing the direction and magnitude of electric fields. The electric field vector at any point is tangent to a field line through that point. The density of field lines in any region is proportional to the magnitude of the electric field in that region. Field lines originate on positive charges and terminate on negative charges. A few examples are shown below: Electric Dipole (电偶极子) Field: An electric dipole consists of two particles with charges of equal magnitude q but opposite sign, separated by a small distance d. It can be proved that the electric field generated by the dipole along the dipole axis is where r is the distance to the center of the dipole r>>d
ElectricFieldsHongKongPolytechnicUniversityDipoleMoment（偶极矩）：p=qd is called the electric dipole moment. It is a vector with a direction pointing fromthenegativetothepositivechargeofthedipole.The electric field in a plane perpendicular to the dipole axis that cuts through thedipole by half isDipoleinanElectricField:The electric field exerts a torque on the dipoleHFThe dipole has a potential energywhere we choose the potential energy to be zero when the angle is 90°
Hong Kong Polytechnic University Electric Fields Dipole Moment (偶极矩): p=qd is called the electric dipole moment. It is a vector with a direction pointing from the negative to the positive charge of the dipole. The electric field in a plane perpendicular to the dipole axis that cuts through the dipole by half is Dipole in an Electric Field: The electric field exerts a torque on the dipole The dipole has a potential energy where we choose the potential energy to be zero when the angle is 90
ElectricFieldsHongKongPolytechnicUniversityElectricField Dueto a Charged Ring:(Optional)AdEdEcosoAs shown in the figure, a is the charge per unit length. The totalcharge on the ring is q.ddE =[dEcos=ldsTSqzqz4元84元(-2 +R2)ElectricFieldDuetoaChargedDisk:(Optional)For a uniformly charged disk with a radius R, we can cut the diskinto small pieces of rings. Suppose the charge per unit area is o,then for each piece of ring, it carries a charge ofEachringcontributesanelectricfieldThe total field is E = [dE =
Hong Kong Polytechnic University Electric Field Due to a Charged Ring: (Optional) As shown in the figure, is the charge per unit length. The total charge on the ring is q. Electric Field Due to a Charged Disk: (Optional) For a uniformly charged disk with a radius R, we can cut the disk into small pieces of rings. Suppose the charge per unit area is , then for each piece of ring, it carries a charge of Each ring contributes an electric field The total field is Electric Fields 3 2 2 2 0 3 0 3 0 3 0 3 0 2 0 4 4 2 4 4 4 1 cos 4 1 cos z R qz r qz R r z ds r z ds r z r dq E dE 2 2 0 0 3 2 2 2 0 1 4 2 z R z z r dr z E dE R
Electric FieldsHongKongPolytechnicUniversityHomework:1.A clock face has negative point charges -g,-2q, -3q, ...,-12g fixed at the positions ofthe corresponding numerals. The clock hands do not perturb the net field due to thepoint charge. At what time does the hour hand point in the same direction as the electricfield vector at the center of the dial? (Hint: Use symmetry).In thefigure a uniform,upward-pointing electric fieldEof magnitude2.00x103N/C hasbeen set up between two horizontal plates by charging the lower platepositively and theupper plate negatively.Theplates have lengthL=10.0 cmand separation d-2.00 cm.Anelectronis then shotbetweentheplates fromtheleft edge ofthelowerplate.Theinitial velocity Voofthe electronmakes an angle -45.0with the lowerplate and has amagnitude of 6.00x106 m/s. (a) Will the electron strike one of the plate? (b)If so,whichplate and howfarhorizontallyfrom the leftedge?H
Hong Kong Polytechnic University Electric Fields Homework: 1. A clock face has negative point charges –q, 2q, 3q, ., 12q fixed at the positions of the corresponding numerals. The clock hands do not perturb the net field due to the point charge. At what time does the hour hand point in the same direction as the electric field vector at the center of the dial? (Hint: Use symmetry). 2. In the figure a uniform, upward-pointing electric field E of magnitude 2.00103 N/C has been set up between two horizontal plates by charging the lower plate positively and the upper plate negatively. The plates have length L=10.0 cm and separation d=2.00 cm. An electron is then shot between the plates from the left edge of the lower plate. The initial velocity v0 of the electron makes an angle =45.0 with the lower plate and has a magnitude of 6.00106 m/s. (a) Will the electron strike one of the plate? (b) If so, which plate and how far horizontally from the left edge?