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Exam2_2003Fall_Solutions

Exam2_2003Fall_Solutions - Physics 8.02 Some(possibly...

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Physics 8.02 Exam Two Mashup Solutions Fall 2003 Some (possibly useful) Relations: F = 1 4 πε o q 1 q 2 r 2 E = q 4 πε o r 2 ˆ r observer to source from points r ˆ = surface closed o inside Q ε dA E outside to inside from points dA = = b a a b b to a from moving V V V ds E 0 = ds E V point charge = q 4 πε o r = = N i i o i q V 1 4 r r πε charges point many V Q C = C Q V = U = 1 2 C V 2 = Q 2 2C I = q n A wire v drift drift wire I qn A = = J v where is the resistivity ρ ρ = E J 1/ where the conductivity σ σ ρ = = = J E V = i R L L R A A ρ σ = = 1 R parallel = 1 R 1 + 1 R 2 R series = R 1 + R 2 R V R i V i P heating ohmic 2 2 = = = (joules/sec) 2 ˆ 4 o q r µ π × = v r B 2 ˆ 4 o I r µ π × = ds r dB G G Ampere’s Law: through o contour I µ = ds B where I through is the current flowing through the open surface bounded by the contour = surface open through I dA J ds right-handed wrt dA F = q v × B ext ext I = × dF ds B The length of an arc of a circle of radius R that subtends an angle θ radians is R θ , right handed with respect to IA I = μ G The area of the sides of a cylinder of radius r and height h is 2 π rh Circular motion: For a particle of mass m to move in a circle of radius R at speed v , there must be an inward force of magnitude R mv 2

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