# oldhw09 - oldhomewk 09 LEE BENJAMIN Due 4:00 am Question 1...

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oldhomewk 09 – LEE, BENJAMIN – Due: Sep 23 2007, 4:00 am 1 Question 1, chap 26, sect 2. part 1 of 2 10 points Two spherical conductors (shown in the fig- ure below) are separated by a distance large enough to make induction effects negligible. The spheres (with radii 1 . 1 cm and 0 . 7 cm) are connected by a thin conducting wire and are brought to the same potential of 775 V relative to 0 V at r = . The Coulomb constant is 8 . 98755 × 10 9 N · m 2 / C 2 . 1 . 1 cm 0 . 7 cm Q 1 Q 2 Determine the capacitance of the system. Correct answer: 2 . 00277 × 10 12 F (tolerance ± 1 %). Explanation: Let : k e = 8 . 98755 × 10 9 N · m 2 / C 2 , R 1 = 1 . 1 cm = 0 . 011 m , and R 2 = 0 . 7 cm = 0 . 007 m . R 1 R 2 Q 1 Q 2 Both spherical conductors are at the same potential V , so V = k e Q 1 R 1 = k e Q 2 R 2 . (1) The charges on the spheres are then Q 1 = V R 1 k e and Q 2 = V R 2 k e . (2) The capacitance of the system is C = Q 1 + Q 2 V (3) = R 1 + R 2 k e = (0 . 011 m) + (0 . 007 m) 8 . 98755 × 10 9 N · m 2 / C 2 = 2 . 00277 × 10 12 F . Question 2, chap 26, sect 2. part 2 of 2 10 points What is the charge ratio Q 1 Q 2 ? Correct answer: 1 . 57143 (tolerance ± 1 %). Explanation: From Eq. 2, Q R , so we have Q 1 Q 2 = R 1 R 2 = 1 . 1 cm 0 . 7 cm = 1 . 57143 . Question 3, chap 26, sect 1. part 1 of 1 10 points A parallel plate capacitor is connected to a battery. + Q - Q d 2 d If we double the plate separation, 1. the capacitance is doubled. 2. the potential difference is halved. 3. the electric field is doubled.

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oldhomewk 09 – LEE, BENJAMIN – Due: Sep 23 2007, 4:00 am 2 4. None of these. 5. the charge on each plate is halved. cor- rect Explanation: The capacitance of a parallel plate capaci- tor is C = ǫ 0 A d .
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