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# 5 - kavo(ak22862 HW05 Janow(12121 This print-out should...

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kavo (ak22862) – HW05 – Janow – (12121) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points The electron volt is a measure of 1. charge. 2. velocity. 3. momentum. 4. energy. correct 5. impulse. Explanation: Electron volt (eV) is a unit commonly used in atomic and nuclear physics. It is defined as the energy that an electron gains or loses by moving through a potential of 1 V. 002 10.0 points Two charges, 2 Q and + Q , are located on the x -axis, as shown below. Point P , at a distance of 3 D from the origin O , is one of two points on the positive x -axis at which the electric potential is zero. x 0 2 Q + Q P D D D How far d from the origin O is the other point? 1. d = 5 4 D 2. d = 7 4 D 3. d = 5 3 D correct 4. d = 8 5 D 5. d = 3 2 D 6. d = 7 5 D 7. None of these 8. d = 6 5 D 9. d = 4 3 D 10. d = 9 5 D Explanation: Suppose the zero-potential point is at a distance d from O. The electric potentials are 2 Q 4 π ǫ 0 | D d | and Q 4 π ǫ 0 | 2 D d | , respectively. For zero electric potential 2 Q 4 π ǫ 0 | D d | + Q 4 π ǫ 0 | 2 D d | = 0 , 2 | D d | = 1 | 2 D d | , which gives d = 5 3 D or d = 3 D . 003 10.0 points A dipole field pattern is shown in the figure. Consider various relationships between the electric potential at different points given in the figure. D J C P T + Notice: Five potential relationships are given below. a) V J = V P > V C b) V J = V P = V C c) V J = V P < V C d) V D < V C < V T

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kavo (ak22862) – HW05 – Janow – (12121) 2 e) V D > V C > V T Which relations shown above are correct? 1. ( a ) only 2. ( a ) and ( e ) only 3. ( c ) and ( d ) only 4. ( b ) and ( e ) only 5. ( c ) only 6. ( b ) and ( d ) only correct 7. ( d ) only 8. ( e ) only 9. ( c ) and ( e ) only 10. ( a ) and ( d ) only Explanation: The electric potential due to one single point charge at a distance r from the charge is given by V = k q r . For a dipole system, the total potential at any place is the sum of potentials due to one positive point charge and one negative point charge (Superposition Principle). From symmetry considerations, it is easy to see that the electric field lines are perpen- dicular to a line which passes through the midpoint C and points J and P . No work needs to be done to move a positive test charge along the midplane because the force and the displacement are perpendicular to each other. V J = V C = V P , relation ( b ). Furthermore, moving along the direction of a electric field line ( i.e. , moving in the direc- tion from positive charge to negative charge along the electric field line) always lowers the electric potential, because the electric field will do positive work to a positive test charge in order to lower its electric potential energy.
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