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Unformatted text preview: Solution for Lab Quiz 12 Capacitance Solution to Lab Quiz Problem 12.1(Energy of Earth) Problem: Modelling the Earth as isolated spherical con ductor with radius 6 . 4 × 10 6 m and electric field of 150 N C downward at its surface. Compute the energy stored in the Earth’s electric field. It is probably easiest to compute the energy from the capacitance. Select One of the Following: (a) 6 . × 10 1 J (b) 5 . 2 × 10 5 J (cAnswer) 3 . 3 × 10 14 J (d) 8 . 85 × 10 12 J (e) 4 . 8 × 10 8 J Solution The capacitance of the earth is C = 4 πε R = 4 π (8 . 85 × 10 12 C 2 Nm 2 )(6 . 4 × 10 6 m) = 7 . 12 × 10 4 F Now we need either the charge or the potential difference with respect to infinity. The electric field of a sphere is kQ R 2 ˆ r = 150 N C ˆ r 1 Solve for Q Q = ER 2 k = (150 N C )(6 . 4 × 10 6 m) 2 8 . 99 × 10 9 Nm 2 C 2 = 6 . 83 × 10 5 C The energy is then U = 1 2 Q 2 C = 1 2 (6 . 83 × 10 5 C) 2 7 . 12 × 10 4 F = 3 . 3 × 10 14 J Total Points for Problem: 3 Points...
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This note was uploaded on 03/29/2010 for the course PHYS 2469 taught by Professor Stewat during the Spring '10 term at University of Arkansas Community College at Batesville.
 Spring '10
 Stewat
 Capacitance, Energy

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