R02_a - REVIEW • ELECTRIC FORCE ELECTRIC FIELD •...

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Unformatted text preview: REVIEW: • ELECTRIC FORCE, ELECTRIC FIELD, • ELECTRIC FIELD LINES, ELECTRIC FLUX, GAUSS’S LAW, • ELECTRIC POTENTIAL, • CONTINUOUS CHARGE DISTRIBUTIONS (ELECTRIC FIELD, ELECTRIC POTENTIAL, GAUSS’S LAW), • ELECTRIC CURRENT, • MAGNETIC FORCE ON MOVING CHARGES AND WIRES, • BIO-SAVART-LAW, • FORCE BETWEEN PARALLEL CURRENT CARRYING WIRES ELECTRIC FORCE: Coulomb’s law: • force on charge 1 due to charge 2 is 12 2 2 1 e 12 ˆ r r q q k F = r Net force on a charge due to several other charges: • VECTOR SUM of all forces on that charge due to other charges • Called Principle of SUPERPOSITON • Each charge exerts a force on charge 1 Resultant force is 41 31 21 1 F F F F r r r r + + = • says net force on charge 1 equals sum of force on 1 from 2, force on 1 from 3, and force on 1 from 4 ELECTRIC FIELD • If the force on q at a point is F r , then electric field at that point is q F E r r = • If the electric field at a point is E r , then the force on q at point is E q F r r = • Electric field at P due to a point charge is r r q k E ˆ 2 e P = r o Unit vector r ˆ points from q → P • Electric field points away from positive charge • Electric field points toward negative charge Superposition: Total E r at point P due to an arrangement of point charges is the VECTOR SUM of the electric field contributions from all charges around P • Total electric field at P is: 4 3 2 1 2 ˆ E E E E r r q k E i i i i e T r r r r r + + + = = ∑ o i q is the charge at i o i r is the distance from i q → P o i r ˆ is the unit vector from i q → P o the sum is a VECTOR SUM Did example with electric dipole ELECTRIC FIELD LINES: • E r vector at a point in space is tangent to the EFL through that point • “Density” of EFL is proportional to E (magnitude) in that region o Larger E → closer packing of lines • EFL start on positive charges and end on negative charges • Number of EFL starting/ending on charge is proportional to its magnitude • Electric field lines do not cross Looked at motion of a particle in a uniform electric field: ELECTRIC FLUX General result for Electric Flux through element of area i A ∆ i i i i i i A E A E r r ∆ ⋅ = ∆ = ∆Φ θ cos E Total flux through a closed surface: ∫ ∫ = ⋅ = Φ dA E A d E n surface closed over E r r GAUSS’S LAW (general statement): enclosed surface closed e ε q A d E ∫ = ⋅ = Φ r r • Powerful way to calculate electric field if we can factor n E out of integral o Trick is to choose surface so that n E is uniform over all or part of surface No charge inside: • net number of lines leaving = 0 • all lines go through Positive charge inside: • non-zero net number of lines leaving • lines start on charge inside sphere Used Gauss’s Law to calculate electric field around a point charge ELECTRIC POTENTIAL Difference in electric potential between points A and B is: q U V V V A B ∆ = − = ∆ SO: ∫ ⋅ − = − = ∆ B A A B s d E V V V r r o Potential difference between two points depends on electric field o Note sign and order of integration limits EQUIPOTENTIAL...
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This note was uploaded on 03/08/2012 for the course PHYSICS 1051 taught by Professor Michaelmorrow during the Winter '12 term at Memorial University.

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R02_a - REVIEW • ELECTRIC FORCE ELECTRIC FIELD •...

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