Exam2_2003Spring

Exam2_2003Spring - Physics 8.02 Some (possibly useful)...

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Physics 8.02 Exam Two Mashup Spring 2003 Some (possibly useful) Relations: inside closedsurface o Q d κ ε ⋅= ∫∫ EA G G w points from inside to outside d A G moving from to b ab b a a VV V ∆= = Es G G d 0 d −⋅= G G v many point charges 1 4 N i i oi q V πε = = rr GG V Q C = C Q V = parallelplate o A C d = U = 1 2 C V 2 = Q 2 2C series 1 2 11 CC =+ 1 C parallel 1 2 C where is the resistivity ρρ = EJ V = i R L R A ρ = 1 R parallel = 1 R 1 + 1 R 2 R series = R 1 + R 2 2 2 ohmic heating V Pi V i R R =∆ = = 2 ˆ 4 o q c r µ π × =< vr Bv G G G < 2 ˆ 4 o I d d r × = sr B G G ˆ points source observer rf r o mt o through contour o dI Bs G G v where I through is the current flowing through any open surface bounded by the contour: through open surface I d = JA G G d s right-handed with respect to d A sgl loop d d N dt dt Φ = Ed s BdA v ext q Fv B G G G ext d Fs B G 2 cent. Fm v = r = perpendicular to loop, right-handed with respect to IA I μn n G ± ± = × τ μ B G G G z zz dB F dz = Cross-products of unit vectors: ˆˆ ˆˆˆˆ 0 ×=×= × = ii jjkk ˆˆ ˆ × = i j k ˆ × = j ki ˆ ×= j Useful integrals: 1/2 2 () d cf f θ + 1 ln( ) d f + 2 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 five 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).
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This note was uploaded on 04/07/2008 for the course 8 8.02 taught by Professor Hudson during the Fall '07 term at MIT.

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Exam2_2003Spring - Physics 8.02 Some (possibly useful)...

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