hw10solution_pdf - klarin(sjk772 – homework 10 – Turner...

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Unformatted text preview: klarin (sjk772) – homework 10 – Turner – (56705) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points A long coaxial cable consists of an inner cylin- drical conductor with radius R 1 and an outer cylindrical conductor shell with inner radius R 2 and outer radius R 3 as shown. The ca- ble extends out perpendicular to the plane shown. The charge on the inner conductor per unit length along the cable is λ and the corresponding charge on the outer conductor per unit length is- λ (same in magnitudes but with opposite signs) and λ > 0. Q R 1 R 2 R 3 b- Q Find the magnitude of the electric field at the point a distance r 1 from the axis of the inner conductor, where R 1 < r 1 < R 2 . 1. None of these. 2. E = λ √ 2 π ǫ r 1 3. E = λ 2 R 1 4 π ǫ r 1 2 4. E = λ 2 π ǫ r 1 correct 5. E = λ 2 π ǫ R 1 6. E = 0 7. E = λ √ 3 π ǫ r 1 8. E = λR 1 3 π ǫ r 1 2 9. E = λR 1 4 π ǫ r 1 2 10. E = 2 λ √ 3 π ǫ r 1 Explanation: Pick a cylindrical Gaussian surface with the radius r 1 and apply the Gauss’s law; we obtain E · ℓ · 2 π r 1 = Q ǫ E = λ 2 π ǫ r 1 002 (part 2 of 2) 10.0 points For a 100 m length of coaxial cable with inner radius 0 . 839574 mm and outer radius 2 . 02841 mm. Find the capacitance C of the cable. Correct answer: 6 . 30673 nF. Explanation: Let : ℓ = 100 m , R 1 = 0 . 839574 mm , and R 2 = 2 . 02841 mm . We calculate the potential across the capaci- tor by integrating-E · d s. We may choose a path of integration along a radius; i.e.,-E · d s =-E dr . V =- 1 2 π ǫ q l integraldisplay R 1 R 2 dr r =- 1 2 π ǫ q l ln r vextendsingle vextendsingle vextendsingle vextendsingle R 1 R 2 = q 2 π ǫ l ln R 2 R 1 . Since C = q V , we obtain the capacitance C = 2 π ǫ l ln parenleftbigg R 2 R 1 parenrightbigg = 2 π (8 . 85419 × 10 − 12 c 2 / N · m 2 ) ln parenleftbigg 2 . 02841 mm . 839574 mm parenrightbigg × (100 m) = 6 . 30673 nF . klarin (sjk772) – homework 10 – Turner – (56705) 2 003 10.0 points Given a spherical capacitor with radius of the inner conducting sphere a and the outer shell b . The outer shell is grounded. The charges are + Q and- Q . A point C is located at r = R 2 , where R = a + b . a A B C + Q- Q b What is the capacitance of this spherical capacitor?...
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hw10solution_pdf - klarin(sjk772 – homework 10 – Turner...

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