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Unformatted text preview: Notes and Solved Problems for Common Exam 1 1. ELECTRIC CHARGE Key concepts: Charged particles attract or repel each other. If particles have charges of the same sign they repel each other. If their charges are of the opposite sign they attract each other. Units of charge: Coulombs. Coulombs Law states that the value of the force between two charged particles Q 1 and Q 2 is proportional to their charges and is inversely proportional to the square of the distance r between them: 1 2 2 Q Q F k r = where coefficient 9 2 2 8.99 10 / k Nm C = which is sometimes expressed via another constant 12 2 2 1 8.85 10 / 4 C Nm k - = = Concept of charge density: for charge Q uniformly distributed over some volume V, the charge per unit volume or volume charge density is the ratio / Q V = . If an object is flat (2 dimensional) the surface charge density is the ratio of the charge Q to the surface area S: / Q S = . For linear, or 1 dimensional objects, the linear charge density is the charge per unit length: / Q L = . We therefore have: 3 : / 2 : / 1 : / D Q V D Q S D Q L = = = These formulas define a uniform distribution. Typical problems related to electric charge: Problem 1. Two electrons are placed at a certain distance between each other? The force between them is: A. Repulsion B. Attraction C. Zero D. Not determined E. None of the above Solution. Two electrons have negative charge, therefore the force is repulsion. Answer A Problem 2. Find force between a proton and an electron placed at the distance 1 m. A. 2.3 * 10-13 N, attraction B. 2.3 * 10-13 N, repulsion C. 2.3 * 10-16 N, attraction D. 2.3 * 10-16 N, repulsion E. 2.3 * 10-9 N, attraction Solution. The force between two oppositely charged particles is attraction and its value is 19 19 9 16 1 2 2 6 2 1.6 10 1.6 10 8.99 10 2.3 10 (10 ) q q F k r---- = = = Answer C. Problem 3 . A postively charged particle with Q= 5 mC is placed between two negatively charged particles with q 1 = 1 mC (left) and q 2 =9 mC (right). The distance between q 1 and q is 5 cm and the distance from q to q 2 is 9 cm. What is the total force acting on the middle particle? Find the value and the direction. A) 3.2 x 10 7 N, left B) 3.2 x 10 7 N, right C) 2.8 x10-9 N, left D) 2.8 x 10-9 N, right E) Zero Solution. The value of the force from particle 1 on the middle particle is 3 3 9 7 1 1 2 2 2 1 1 10 5 10 8.99 10 1.8 10 (5 10 ) q Q F k r--- = = = The direction of this force is to the left since particle 1 and the middle particle are oppositely charged and attract each other. The value of the force from particle 2 on the middle particle is 3 3 9 7 2 2 2 2 2 2 9 10 5 10 8.99 10 5.0 10 (9 10 ) q Q F k r--- = = = The direction of this force is to the right since particle 2 and the middle particle are oppositely charged, and this force is attractive too, but points in the opposite direction. If we choose the x-axis from the left to the right, the force F1 has a minus sign (since its...
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