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 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 G G 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 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 I AI = μ G 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 magnitude R mv 2
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Problem 1 (25 Points) Circle your choice for the correct answer to the five questions below. A: A segment of a wire of length dl carries a current I (see sketch below). The unit vector points out of the page. ˆ z The magnetic field due to this wire segment at the location P shown in the sketch is dB G 1. 3/2 22 ˆ 4 o I adl ab µ π ⎡⎤ + ⎣⎦ z 2. ˆ 4 o I + z 3. ˆ 4 o I bdl + z 4. ˆ 4 o I + z B: A ring of current carrying current clockwise as seen from above sits beneath the South pole of a permanent magnet. The force on the ring of current is 1. Upward 2. 3. Zero
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8.02 2 nd Exam Name_____________________ Fall 2003 Solutions 2 C: Two charged particles of identical charge move in circular orbits in the same constant magnetic field z B . The two particles have the same speed but different masses. ˆ o B = The orbit of the particle with the larger mass will: 1. have a larger radius and a longer period as compared to that of the lighter particle 2. have a smaller radius and a shorter period as compared to that of the lighter particle 3. have a larger radius and a shorted period as compared to that of the lighter particle 4. have a smaller radius and the a longer period as compared to that of the lighter particle D: A circuit in the form of a circular loop of wire sits in a spatially uniform magnetic field that is pointing downward. The magnitude of the magnetic field is decreasing with time. Thus, 1. The induced current in the loop is clockwise and the net magnetic force on the loop is upward.
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Exam2_2003Fall_Solutions - Physics 8.02 Some (possibly...

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