Homework 6 Solutions

Thus c hc hc h j 2 1014 m 32 1019 c 10 105 m

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Unformatted text preview: s q = 2e = 2(1.60 × 10–19 C) = 3.20 × 10–19 C, and the drift speed is 1.0 × 105 m/s. Thus, c hc hc h J = 2 × 1014 / m 3.2 × 10−19 C 10 × 105 m / s = 6.4 A / m2 . . (b) Since the particles are positively charged the current density is in the same direction as their motion, to the north. (c) The current cannot be calculated unless the cross-sectional area of the beam is known. Then i = JA can be used. 6. (a) Circular area depends, of course, on r2, so the horizontal axis of the graph in Fig. 26-23(b) is effectively the same as the area (enclosed at variable radius values), except for a factor of π. The fact that the current increases linearly in the graph means that i/A = J = constant. Thus, the answer is “yes, the current density is uniform.” (b) We find i/(πr2) = (0.005 A)/(π × 4 × 10−6 m2) = 398 ≈ 4.0 × 102 A/m2. 7. The cross-sectional area of wire is given by A = πr2, where r is its radius (half its thickness). The magnitude of the current density vector is J = i / A = i / π r2, so 1041 i 0.50 A = = 1.9 ×10−4 m. 4 2 πJ π ( 440 ×10 A/m ) r= The diameter of the wire is therefore d = 2r = 2(1.9 × 10–4 m) = 3.8 × 10–4 m. 8. (a) The magnitude of the current density vector is 4 (1.2 ×10−10 A ) i i J= = = = 2.4 ×10−5 A/m 2 . 2 2 −3 A π d / 4 π ( 2.5 ×10 m ) (b) The drift speed of the current-carrying electrons is J 2.4 × 10−5 A / m2 vd = = = 18 × 10−15 m / s. . 28 3 −19 ne 8.47 × 10 / m 160 × 10 C . c hc h 9. We note that the radial width Δr = 10 μm is small enough (compared to r = 1.20 mm) that we can make the approximation ∫ Br 2π rdr ≈ Br 2π r Δr Thus, the enclosed current is 2πBr2Δr = 18.1 μA. Performing the integral gives the same answer. 10. Assuming J is directed along the wire (with no radial flow) we integrate, starting with Eq. 26-4, R 1 (kr 2 )2π rdr = kπ ( R 4 − 0.656 R 4 ) i = ∫ | J | dA = ∫ 9 R /10 2 where k = 3.0 × 108 and SI units are understood. Therefore, if R = 0.00200 m, w...
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This document was uploaded on 02/26/2014 for the course PHYS 2b at UCSD.

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