# HW10 - yang(ey942 – oldhomework 10 – Turner –(56705 1...

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Unformatted text preview: yang (ey942) – oldhomework 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 4) 10.0 points An air-filled capacitor consists of two parallel plates, each with an area of 10 cm 2 , sepa- rated by a distance 5 mm . A 30 V potential difference is applied to these plates. The permittivity of a vacuum is 8 . 85419 × 10 − 12 C 2 / N · m 2 . 1 pF is equal to 10 − 12 F . The magnitude of the electric field between the plates is 1. E = parenleftbigg d V parenrightbigg 2 . 2. E = parenleftbigg V d parenrightbigg 2 . 3. E = 1 ( V d ) 2 . 4. None of these 5. E = V d . 6. E = 1 V d . 7. E = ( V d ) 2 . 8. E = V d . correct 9. E = d V . Explanation: Since E is constant between the plates, V = integraldisplay vector E · d vector l = E d E = V d . 002 (part 2 of 4) 10.0 points The magnitude of the surface charge density on each plate is 1. σ = ǫ ( V d ) 2 . 2. σ = ǫ V d . correct 3. σ = ǫ ( V d ) 2 . 4. σ = ǫ parenleftbigg d V parenrightbigg 2 . 5. σ = ǫ d V . 6. σ = ǫ V d 7. None of these 8. σ = ǫ parenleftbigg V d parenrightbigg 2 . 9. σ = ǫ V d . Explanation: Use Gauss’s Law. We find that a pillbox of cross section S which sticks through the sur- face on one of the plates encloses charge σ S. The flux through the pillbox is only through the top, so the total flux is E S. Gauss’ Law gives σ = ǫ E = ǫ V d Alternatively, we could just recall this result for an infinite conducting plate (meaning we neglect edge effects) and apply it. 003 (part 3 of 4) 10.0 points Calculate the capacitance. yang (ey942) – oldhomework 10 – Turner – (56705) 2 Correct answer: 1 . 77084 pF. Explanation: Let : A = 0 . 001 m 2 , d = 0 . 005 m , V = 30 V , and ǫ = 8 . 85419 × 10 − 12 C 2 / N · m 2 . The capacitance is given by C = ǫ A d = 8 . 85419 × 10 − 12 C 2 / N · m 2 × . 001 m 2 . 005 m = 1 . 77084 × 10 − 12 F = 1 . 77084 pF ....
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## This note was uploaded on 11/21/2010 for the course PHY 56705 taught by Professor Turner during the Spring '10 term at University of Texas.

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HW10 - yang(ey942 – oldhomework 10 – Turner –(56705 1...

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