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Homework 5-solutions

# Homework 5-solutions - soto(rrs946 Homework 5 Homann(56605...

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soto (rrs946) – Homework 5 – Hoffmann – (56605) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0points A 43 m length of coaxial cable has a solid cylindrical wire inner conductor with a di- ameter of 3 . 558 mm and carries a charge of 12 . 34 μ C. The surrounding conductor is a cylindrical shell and has an inner diameter of 11 . 188 mm and a charge of - 12 . 34 μ C. Assume the region between the conductors is air. The Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 . What is the capacitance of this cable? Correct answer: 2 . 08808 nF. Explanation: Let : k e = 8 . 98755 × 10 9 N · m 2 / C 2 , Q = 12 . 34 μ C , = 43 m , a = 3 . 558 mm , and b = 11 . 188 mm . The charge per unit length is λ Q . V = - integraldisplay b a vector E · dvectors = - 2 k e λ integraldisplay b a dr r = - 2 k e Q ln parenleftbigg b a parenrightbigg . The capacitance of a cylindrical capacitor is given by C Q V = 2 k e 1 ln parenleftbigg b a parenrightbigg = 43 m 2 (8 . 98755 × 10 9 N · m 2 / C 2 ) × 1 ln parenleftbigg 11 . 188 mm 3 . 558 mm parenrightbigg · parenleftbigg 1 × 10 9 nF 1 F parenrightbigg = 2 . 08808 nF 002 10.0points A parallel-plate capacitor is charged by con- necting it to a battery. If the battery is disconnected and then the separation between the plates is increased, what will happen to the charge on the capac- itor and the electric potential across it? 1. The charge increases and the electric po- tential decreases. 2. The charge increases and the electric po- tential remains fixed. 3. The charge and the electric potential de- crease. 4. The charge and the electric potential in- crease. 5. The charge remains fixed and the electric potential increases. correct 6. The charge decreases and the electric po- tential increases. 7. The charge remains fixed and the electric potential decreases. 8. The charge and the electric potential re- main fixed.

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