January 12, 2005 Physics for Scientists&Engineers 2 1Physics for Scientists &Physics for Scientists &EngineersEngineers 22Spring Semester 2005Lecture 4January 12, 2005 Physics for Scientists&Engineers 2 2The Electric FieldThe Electric Field! For the past three days we have been discussingthe force between two charges that we not movingwith respect to each other! Suppose one charge were moving, how would thesecond charge know that the first charge hadmoved?! What if there were other charges, how would onecharge know about the extra charges?! To deal with these situations, we introduce theconcept of a fieldJanuary 12, 2005 Physics for Scientists&Engineers 2 3The Electric Field (2)The Electric Field (2)! A field is an abstract concept that we can use todescribe forces! The electric field is defined at any point in spaceas the force of the electric field on a positivepoint charge! If we place a positive point charge in an electricfield, there will be a vector force on that charge inthe direction of the electric field• The magnitude of the force is given by the strength ofthe electric fieldJanuary 12, 2005 Physics for Scientists&Engineers 2 4Definition of Electric FieldDefinition of Electric Field! We define the electric field in terms of the force it exertson a positive point charge! The unit of the electric field are N/C (newtons percoulomb)! We can then write! We see that the electric force is parallel to the electricfield and is proportional to the charge• The force on a negative charge will be in the opposite direction !E =!Fq !F = q!EJanuary 12, 2005 Physics for Scientists&Engineers 2 5Superposition of Electric FieldsSuperposition of Electric Fields! Suppose we have many charges! The electric field at any point in space will havecontributions from all the charges! The electric field at any point in space is thesuperposition of of the electric field from ncharges is! Note that the superposition applies to eachcomponent of the field !E =!E1+!E2+!E3+ ... +!EnJanuary 12, 2005 Physics for Scientists&Engineers 2 6Electric Field LinesElectric Field Lines! We can represent the electric field graphically bydrawing lines that represent the vector forceexerted on a positive test charge! Electric field lines will originate on positivecharges and terminate on negative charges! Electric fields exist in three dimensions, but weoften show a two-dimension representation! Electric field lines do not cross! The electric force at a given point in space istangent to the electric field linesJanuary 12, 2005 Physics for Scientists&Engineers 2 7Properties of Field LinesProperties of Field Lines! The strength of the electric field is represented by thedensity of electric field lines! The direction of the electric field is tangent to theelectric field linesStrongWeakJanuary 12, 2005 Physics for Scientists&Engineers 2 8Field Lines from a Point ChargeField Lines from a Point Charge! The electric field linesfrom a point chargeextend out radially! For a positive pointcharge, the field linespoint outward• Terminate at infinity! For a negative charge,the field lines pointinward• Originate at infinityJanuary 12, 2005 Physics for Scientists&Engineers 2 9Electric FieldElectric Field Lines for Two Point ChargesLines for Two Point Charges! We can use the superposition principle to calculate theelectric field from two point charges! Let’s start with one positive charge and one negative charge! The field lines will originate from the positive charge andterminate on the negative chargeJanuary 12, 2005 Physics for Scientists&Engineers 2 10Electric Field Lines fromElectric Field Lines from Identical Point ChargesIdentical Point Charges! Now let’s look at the electric field from two identical point charges! For two positive charges, the field lines originate on the positivecharges and terminate at infinity! For two negative charges, the field lines terminate on the negativecharges and originate at infinityJanuary 12, 2005 Physics for Scientists&Engineers 2 11General Observations about Field LinesGeneral Observations about Field Lines! If the field lines connect, we havean attractive force• You can imagine the charges pulling oneach other! If the field lines seem to spreadout, we have a repulsive force• You can imagine the charges pushingeach other apart! Field lines always originate on positive charge andterminate on negative charge! Field lines never cross! http://lectureonline.cl.msu.edu/~mmp/kap18/RR447app.htmJanuary 12, 2005 Physics for Scientists&Engineers 2 12Example - Force from FieldExample - Force from Field LinesLines! What are the magnitudes (high, medium, low) and thedirection of the electric force for the following fourcases:1) +q at a)2) +q at b)3) -q at c)4) -q at
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