# The Electric Field

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Phys102 Lecture 2The Electric FieldKey Points Coulomb’s Law The electric field (E is a vector!)ReferencesTextbook: 16-1,2,3,4,5,6,7,8,9, .Phys102 Lecture 2 - 1

The Electric FieldThe electric field is defined as the force on a smallcharge, divided by the magnitude of the charge:

The Electric FieldAn electric field surrounds every charge.

The Electric FieldFor a point charge:The magnitude of the electric field due to charge Q :1 QE 4 0 r 2

The Electric FieldForce on a pointcharge in anelectric field:

Example: Electric field above two point charges.Calculate the total electric field (a) at point A and (b) at point B in thefigure due to both charges, Q1 and Q2.

Example: Electric field above two point charges.Calculate the total electric field (a) at point A and (b) at point B in thefigure due to both charges, Q1 and Q2.

Problem solving in electrostatics: electricforces and electric fields1. Draw a diagram; show all charges, withsigns, and electric fields and forces withdirections.2. Calculate forces using Coulomb’s law.3. Add forces vectorially to get result.4. Check your answer!

Field LinesThe electric field can be represented by fieldlines. These lines start on a positive chargeand end on a negative charge.

Field LinesThe number of field lines starting (ending)on a positive (negative) charge isproportional to the magnitude of the charge.The electric field is stronger where the fieldlines are closer together.

Field LinesElectric dipole: two equal charges, opposite insign:

Field LinesThe electric field betweentwo closely spaced,oppositely charged parallelplates is constant.

Field LinesSummary of field lines:1. Field lines indicate the direction of thefield; the field is tangent to the line.2. The magnitude of the field is proportionalto the density of the lines.3. Field lines start on positive charges andend on negative charges; the number isproportional to the magnitude of thecharge.

Electric Fields and ConductorsThe static electric field inside a conductor is zero – ifit were not, the charges would move.The net charge on a conductor resides on its outersurface.

Electric Fields and ConductorsThe electric field is perpendicular to thesurface of a conductor – again, if it were not,charges would move.

Electric Fields and ConductorsConceptual Example:Shielding, and safetyin a storm.A neutral hollowmetal box is placedbetween two parallelcharged plates asshown. What is thefield like inside thebox?

i-clicker quiz 2-1A metal ball hangs from the ceiling byA) positivean insulating thread. The ball isB) negativeattracted to a positive-charged rod heldC) neutralnear the ball. The charge of the ballmust be:D) positive or neutralE) negative or neutral

Van de Graaff GeneratorThe electric field is defined as the force on a smallcharge, divided by the magnitude of the charge:

i-clicker 2-2Two neutral conductors are connectedA)00by a wire and a charged rod is broughtB) –C)– D) E)––near, but does not touch. The wire istaken away, and then the charged rodis removed. What are the charges onthe conductors?00?

i-clicker 2-3F1 3 NQQF2 ?A) 3/4 NB) 3.0 NC) 12 ND) 16 NF1 ?4QQF2 ?E) 48 NIf we increase one charge to 4Q,what is the magnitude of F1?

i-clicker 2-4The force between two chargesA) 9Fseparated by a distance d is F. IfB) 3Fthe charges are pulled apart to aC) Fdistance 3d, what is the force onD) 1/3Feach charge?E) 1/9FF?QQFdQQ3d?

i-clicker 2-5You are sitting a certain distance froma point charge, and you measure anelectric field of E0. If the charge isdoubled and your distance from thecharge is also doubled, what is theelectric field strength now?A) 4E0B) 2E0C) E0D) 1/2E0E) 1/4E0

i-clicker 2-6-Q QWhat is the direction ofthe electric field at theposition of the X ?2314 QA) 1B) 2C) 3D) 4E) 55

The electric field between two closely spaced, oppositely charged parallel plates is constant. Field Lines . Summary of field lines: 1.Field lines indicate the direction of the field; the field is tangent to the line. 2.Th

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