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PH112 EXAM III Winter Quarter 2005-06 Name:________________ Box: No:______ Answer all questions. Do not erase your work. If you need more space work the problems on the back. All questions are 25 points each. Equation sheet is provided at the end of the exam. Problems Score 1 (25 points) 2 (25 points) 3 (25 points) 4 (25 points) Total (100 points) 1 1. Two point charges -3.0 C and 9.0 C are placed along the x axis as shown in the figure. a) Sketch the electric field lines in the figure. Make sure to show how the strength of the charges modifies the electric field. -3 C 9 C 5m b) Determine the position where the electric field is zero along the x axis. E(9μC) k.9μC (5 x) 2 E(9μC) E(3μC) k.9μC (5 x) E(3μC) k.9μC (5 x) 2 k.3μC ( x) 2 k.3μC ( x) 2 k.3μC ( x) Solving for x, we get x = 6.83m c) Determine the electric potential at a distance of 1.00 m along the x-axis away from the 9.0 C charge towards the left. k.9μC 1.00 V (9μC) 80,910 V V (9μC) k.(3μC) 6.00 V (3μC) 4495 V V (3μC) V 76,415 V 2 2. A sphere of radius 10.0cm has a charge +20C uniformly distributed through out the volume and is concentric with a spherical conducting shell of inner radius 20.0cm and outer radius 30.0cm. This outer shell has a net charge of -40C. Find the electric field, a) within the sphere at r = 8 cm; 10 cm 4 q(enclosed ) ρ( (0.008) 3 ) 3 where ρ 20μC 4 (0.01) 3 3 q(enclosed ) 10.24 μC E dA q(enclosed ) o E(4πr 2 ) q(enclosed ) r 0.08m o E 1.44 x10 7 N / C 30 cm 20 cm b) between the sphere and the shell at r = 15cm; q(enclosed ) 20 μC E dA q(enclosed ) o E(4πr 2 ) q(enclosed ) r 0.15m o E 7.99x10 6 N / C c) outside the shell at r = 35.0cm. q(enclosed ) 20 μC E dA q(enclosed ) o E(4πr 2 ) q(enclosed ) r 0.35m o E 1.47 x10 6 N / C d) What are the charges on the inner and outer surface of the shell? q(inner) 20 μC q(outer) 20 μC 3 3. The following figure shows a plastic rod of length L = 0.5m and uniform positive charge 10.0 C lying on an axis. a) With V = O at infinity, find the electric potential at point P at a distance d = 1.00m from center of the rod. dq λdx dV 10μC 0.5 kλdx P kdq 1 r (1 x 2 ) 2 V kλ log x x 2 1 V 77,295 V V dV kλdx 2 (1 x ) 1 2 kλ 0.25 dx 0.25 (1 x2) 1 2 limits from - 0.25 to 0.25 r d x dx L b) If a charge of 5 C is moved away from point P by 0.5 m, how much work must be done on that charge? c) How much work is done if the 5 C is moved closer to the line of charges by 0.5 m? 4 4. A small sphere of mass 2.00 g hangs by a thread between two parallel vertical plates 8.00 cm apart. The charge on the sphere is 22.0 x 10-6 C. a) Sketch the electric field lines inside the two plates. b) What potential difference between the plates will cause the thread to assume an angle of 40 degrees with the vertical? T cos(40) mg (1) T sin(40) qE (2) qE tan( 40) mg _ + By using equations 1 and 2 mgtan(4) 2 x10 3 x 9.81xtan(40) q 22.0 x10 6 E 748.3 V/m E T V Ed 748.3x0.08 59.9 V o 40 qE mg c) What happens if the mass of the sphere is increase by a factor of 2? 748.3 V/m 4x10 -3 x 9.81x tan( ) 22.0 x10 6 22 o 5 PH112 PHYSICS EQUATIONS E F qo E 2o 1 q1q2 rˆ 4 r 2 o 1 p E 4 z 3 1 q rˆ 4 r 2 o 1 q V 4o r F qE Va V - E . dl b F E o b a p x E o qencl n q 1 i 4o i 1 ri 1 dq V 4o r E.A U E.dA U qV V Ex x V (total) U p.E E E o 2o r 1 q1q2 4o r Ey V y k = 8.988 x 109 N. m2/C2 o = 8.854 x 10-12 C2/N.m2 e = 1.6021 x 10-19 C 6 Ez V z