Physics 2102 Lecture: 03 FRI 16 JANWhat Are We Going to Learn? A Road MapCoulomb’s LawE-Field is E-Force Divided by E-ChargeElectric FieldsSuperposition of F and EExampleElectric Field LinesDirection of Electric Field LinesElectric Field of a DipoleElectric Field On Axis of DipoleSlide 12Force on a Charge in Electric FieldSlide 14Electric Dipole in a Uniform FieldPowerPoint PresentationJanuary 14, 2019 Physics 2102 Physics 2102 Lecture: 03 FRI 16 JAN Lecture: 03 FRI 16 JAN Electric Fields IElectric Fields IMichael Faraday (1791-1867)Physics 2102Jonathan DowlingVersion: 01/14/19QuickTime™ and a decompressorare needed to see this picture.QuickTime™ and a decompressorare needed to see this picture.What Are We Going to What Are We Going to Learn?Learn?A Road MapA Road Map•Electric charge - Electric force on other electric charges- Electric field, and electric potential•Moving electric charges : current •Electronic circuit components: batteries, resistors, capacitors•Electric currents - Magnetic field - Magnetic force on moving charges•Time-varying magnetic field Electric Field•More circuit components: inductors. •Electromagnetic waves - light waves•Geometrical Optics (light rays). •Physical optics (light waves)2q−12F1q+21F12rCoulomb’s LawCoulomb’s Law2122112||||||rqqkF =2212001085.8with 41mNCk−×== επε2291099.8CmN×k =For Charges in aVacuumOften, we write k as:E-Field is E-Force Divided by E-Field is E-Force Divided by E-ChargeE-ChargeDefinition of Electric Field: € r E =r F q € |r F 12|=k | q1| | q2|r122+q1–q2 € r F 12P1P2 € |r E 12|=k | q2|r122–q2 € r E 12P1P2Units: F/=/[N]/=/[Newton] ; E/=/[N/C]/=/[Newton/Coulomb]E-Force on ChargeE-Field at PointElectric FieldsElectric Fields•Electric field E at some point in space is defined as the force experienced by an imaginary point charge of +1 C, divided by 1 C.•Note that E is a VECTOR.•Since E is the force per unit charge, it is measured in units of N/C. •We measure the electric field using very small “test charges”, and dividing the measured force by the magnitude of the charge. 2||||RqkE =–qRE+1CElectric Field of a Point ChargeSuperposition of F and Superposition of F and EE•Question: How do we figure out the force or field due to several point charges?•Answer: consider one charge at a time, calculate the field (a vector!) produced by each charge, and then add all the vectors! (“superposition”)•Useful to look out for SYMMETRY to simplify calculations!Example •4 charges are placed at the corners of a square as shown. •What is the direction of the electric field at the center of the square?(a) Field is ZERO!(b) Along +y(c) Along +x-q-2q+2q+qyxTotal electric fieldElectric Field Lines •Field lines: useful way to visualize electric field E•Field lines start at a positive charge, end at negative charge•E at any point in space is tangential to field line•Field lines are closer where E is strongerExample: a negative point charge — note spherical symmetryDirection of Electric Field Lines E-Field Vectors Point Away from Positive Charge — Field Source!E-Field Vectors Point Towards Negative Charge — Field Sink!Electric Field of a Electric Field of a DipoleDipole •Electric dipole: two point charges +q and –q separated by a distance d•Common arrangement in Nature: molecules, antennae, …•Note axial or cylindrical symmetry•Define “dipole moment” vector p: from –q to +q, with magnitude qdCancer, Cisplatin and electric dipoles:http://chemcases.com/cisplat/cisplat01.htmQuickTime™ and aCinepak decompressorare needed to see this picture.Electric Field On Axis of Electric Field On Axis of DipoleDipole−++= EEE :ionSuperposit22⎟⎠⎞⎜⎝⎛−=+axkqE22⎟⎠⎞⎜⎝⎛+−=−axkqE⎥⎥⎥⎥⎦⎤⎢⎢⎢⎢⎣⎡⎟⎠⎞⎜⎝⎛+−⎟⎠⎞⎜⎝⎛−=222121axaxkqE22242⎟⎟⎠⎞⎜⎜⎝⎛−=axxakqPax-q+qax-q+qElectric Field Electric Field OnOn Axis Axis of Dipoleof Dipole2222224242⎟⎟⎠⎞⎜⎜⎝⎛−=⎟⎟⎠⎞⎜⎜⎝⎛−=axkpxaxxakqEWhat if x>> a? (i.e. very far away)p = qa“dipole moment”a VECTOR - +3422xkpxkpxE =≈EG=Gp/r3 is actually true for ANY point far from a dipole (not just on axis)3rpErr∝Force on a Charge in Force on a Charge in Electric FieldElectric FieldDefinition of Electric Field: € r E =r F qForce on Charge Due to Electric Field: € r F = qr EForce on a Charge in Force on a Charge in Electric FieldElectric FieldEEPositive Charge Force in Same Direction as E-Field Negative Charge Force in Opposite Direction as E-Field + + + + + + + + + + + + + + + + + + – – – – – – – – – – – – – – – – – – – –Electric Dipole in a Electric Dipole in a Uniform FieldUniform Field•Net force on dipole = 0; center of mass stays where it is.•Net TORQUE : INTO page. Dipole rotates to line up in direction of E.•| | = 2(qE)(d/2)(sin ) = (qd)(E)sin = |p| E sin = |p x E| •The dipole tends to “align” itself with the field lines. •What happens if the field is NOT UNIFORM??Distance Between Charges = dQuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this
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