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Exam2_2004Spring_Solutions

# Exam2_2004Spring_Solutions - Physics 8.02 Exam Two Mashup...

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Physics 8.02 Exam Two Mashup Solutions Spring 2004 Some (possibly useful) Relations: = 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 = = 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 = qn A wire v drift drift wire I qn A == Jv where is the resistivity ρ = EJ 1/ where the conductivity σ σρ = JE V = i R L L R A A 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 × = vr B 2 ˆ 4 o I r × = ds r dB ˆ points source observer rf r o mt o through o contour I = ds B where I through is the current flowing through the open surface bounded by the contour center of circle of radius 2 o a I B a = = surface open through I dA J ds right-handed wrt dA F = q v × B ext ext I = × dF ds B Cross-products of unit vectors: ˆˆ ˆˆˆˆ 0 ×=×= × = ii jjkk ˆˆ ˆ × = ijk ˆ × =− ik j ˆ ×= j ki Useful integrals: 1/2 2 () d cf f θ =+ + 1 ln( ) d f + 2 11 d fcf ++ Useful Small Argument Approximations (1 ) 1 for <<1 n n εε +≅ + ln(1 ) for <<1 +

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8.02 2 nd Exam Name_____________________ Problem 1 (25 Points) Circle your choice for the correct answer to the six questions below. A: Eight parallel wires cut the page perpendicularly at the points shown. All the wires carry the same magnitude of current 0 I , but some carry current into the page and some carry current out of the page. For wires 1 to 4, the current flows up out of the page; for the rest, the current flows down into the page. If we valuate d Bs G G v along the closed path (see figure) in the direction indicated by the arrowhead, we get (a) 4 oo I µ (b) 3 I (c) 2 I (d) I (e) 0 CORRECT (f) I (g) 2 I (h) 3 I (i) 4 I B: A wire loop carries current I 1 , and is located near an infinite wire carrying current I 2 . The currents flow in the directions shown. The net force on the wire loop due to the presence of the infinite wire is (a) upwards CORRECT (b) downwards (c) 0 (d) to the left (e) to the right Spring 2004 Mashup Solutions Page 2
8.02 2 nd Exam Name_____________________ Spring 2004 Mashup Solutions Page 3 C. Consider two identical circular loops of radius a , separated by a distance a , with the second (right hand) coil rotated slightly clockwise relative to the first when looking from above: Top view Side view A large current is suddenly injected into the left hand loop. What happens to the right

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Exam2_2004Spring_Solutions - Physics 8.02 Exam Two Mashup...

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