Electrostatic Forces and Fields

Transcription

1 Conductors, Insulators, and Induced Charges Electrostatic orces and ields undamental unit of charge is the Coulomb (C) electron charge is 1.60 x C proton charge is 1.60 x C Conductors permit easy moement of charge. Insulators do not. Charges can be transferred to materials as well as be induced within the material. 1 2 The Electrostatic orce orce between stationary electric charges orce can be attractie or repulsie Like charges repel (,) or (,) Unlike charges attract (,) or (,) where: = 1 q 1 k = 1 N $ m 2 = 9.0 x 10 9 C 2 Electrostatic orce between q 1 and (N)! " Permittiity of free space (8.85 x C 2 /N m 2 ) r Distance between q 1 and (m) q i Electrostatic charge on object i (C) 3 4 = k 2, 1 Both charges experience the same force. r 2, 1 i, j is the force that charge i exerts on charge j. 2, 1 The forces are ectors and i, j = " j,i 5 6

2 (Vector orm) 1,2 = 1 q 1 (Vector orm) 2,1 = 1 q 1 where is a unit ector directed from q 1 to where is a unit ector directed from to q 1 1,2 = i ˆ r 1,2 2, 1,1 2,1 = "ˆ i 7 8 (Vector orm) 1,2 = 1 q 1 (Vector orm) 2,1 = 1 q 1 where is a unit ector directed from q 1 to where is a unit ector directed from to q 1 1,2 = i ˆ r 1,2 2, 1 r 2,1 2,1 = "ˆ i 9 10 Charging by Conduction If a negatielycharged conductor is brought into contact with a neutral conductor, electrons are transferred to the neutral conductor and it becomes charged by conduction. Induction If a negatielycharged object is brought near a neutral conductor the mobile electrons in the conductor will be repelled, leaing behind positiely charged nuclei. Charged Conductor Neutral Conductor Charging by Conduction Charged Object Neutral Conductor 11 12

3 Charge separation can be used to charge an object without touching it. Charge separation can be used to charge an object without touching it. Electron transfer Charged Rod If the spheres are separated while the rod is nearby, each sphere will hae an equal and opposite charge. Charged Rod After remoing the charged rod: Positiely Charged Negatiely Charged Positiely Charged Negatiely Charged This process is called charging by induction An electric field extends outward from a charged object and permeates all of space. The electric field at some point near a charged object is defined to be the electrostatic force per unit charge acting on the charge placed at that point. The electric field is a ector field and the direction of electric field is that of the electrostatic force acting on the positie test charge. where: E acting on test charge (N/C) Electrostatic force acting on charge (N) magnitude of the test charge (C) 17 18

4 19 20 q = 1 q = 1 q = 1 q due to a Point Charge 1 q r 2 is a unit ector that points along the line from source point to field point. or a system of point charges the electric field can be found by summing up the indiidual contributions ield Lines ield lines proide a graphical representation of electric fields. At any point on a field line, the tangent to the line is the direction of the electric field at that point Where the lines are closer together, E is larger ield lines point away from positie charges and towards negatie charges When charge is distributed oer a line, a surface, or through a olume we often speak of linear charge density # (C/m) surface charge density $ (C/m 2 ) olume charge density % (C/m 3 ) de = 1 dq r

5 de = 1 dq r 2 Since the electric field is a ector the x and y components must be treated separately. " de = 1 dq " 4#$ o 1 dq $ de x = decos" de y = desin" or a total charge Q uniformly distributed oer a length L " = Q L or linear charge distributions (line charges) dq = "dl or uniform charge distributions along the xaxis dq = "dx or uniform charge distributions along the yaxis dq = "dy or circular uniform charge distributions radius R dq = "ds = "Rd# or a uniformly charged surface total charge Q and area A " = Q A or a uniformly charged olume total charge Q and olume V " = Q V or surface charge distributions (charged plates) dq = "da or olume charge distributions (charged solids) dq = "dv 29 30