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PH112 EXAM III -Sample 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. Equation sheet is provided at the end of the exam. Problems Score 1 (25 points) 2 (25 points) 3 (25 points) Total (75 points) 1 1. A conducting rod having uniformly distributed charge is bent to a 180 degree circular arc of radius 10 cm. One half of the plastic rod has +500 nC of charge and the other half has -250 nC of charge. A switch prevents the charges from migrating and canceling out the negative charges. a) Sketch the electric field components at point P in the diagram. Determine the direction of the electric field from the figure. -250 nC 500 nC p Switch b) Determine the electric field at the center of the of the circle when the switch is closed. Assume that the resultant charges are uniformly distributed along the whole 180 degree segment. Do not substitute numbers in the equation in the beginning. 2 2. 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 one end of the rod. d L P b) If a charge of 5 C is brought from infinity to the point P what is the electric potential energy acquired by the charge? c) If a charge of 5 C is brought from infinity to minus infinity and then to point P what is the electric potential energy acquired by the charge? 3 4. The electric potential in a region of space is given by V(x,y,z) = A(x 2 .y + y2 .z z.x.y), where A is a constant. a) Determine the electric field E at any given point in this region. b) The work done by the field when a 1.50 C charge moves through from the point (0, 0, 0.250 m) to the origin is measured to be 100 J. Determine the constant A. c) Determine the electric field at point (0, 0, 0.250m). d) If the point of observation is moved away from the origin along the x-axis does the electric field increase or decrease? 4 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 5 Ez V z