Exam2_2003Spring_Solutions

Exam2_2003Spring_Solutions - Physics 8.02 Exam Two Mashup...

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Physics 8.02 Exam Two Mashup Solutions Spring 2003 Some (possibly useful) Relations: F = 1 4 πε o q 1 q 2 r 2 E = q 4 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 o r = = N i i o i q V 1 4 r r 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 Ampere’s Law: through o contour I = 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 Circumferences, Areas, Volumes: 1) The area of a circle of radius r is r 2 Its circumference is 2 r 2) The area of a sphere of radius r is 4 r 2 . Its volume is 3 3 4/ r The area of the sides of a cylinder of radius r and height h is 2 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
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NAME______________________ page 2 magnitude R mv 2
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8.02 2 nd Exam Name_____________________ Spring 2003 Solutions Page 3 Problem 1 (25 Points) Circle your choice for the correct answer to the six questions below. A: A current I is uniformly distributed over the cross-section of a conducting wire of radius a . For distances r from the center of the wire with r < a , 1. The magnitude of the magnetic field does not depend on r . 2. The magnitude of the magnetic field is proportional to 1/r 3. The magnitude of the magnetic field is proportional to r 4. The magnitude of the magnetic field is proportional to 1/r 2 5. The magnitude of the magnetic field is proportional to r 2 B: A segment of a wire of length dl carries a current I (see sketch below). The magnitude of the magnetic field due to this wire segment at the location P shown in the sketch is 1. [] 2 / 3 2 2 4 b a dl a I o + π µ 2.
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Exam2_2003Spring_Solutions - Physics 8.02 Exam Two Mashup...

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