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HW07solutions

# HW07solutions - 29.28 Model The electric potential at the...

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29.28. Model: The electric potential at the dot is the sum of the potentials due to each charge. Visualize: Please refer to Figure EX29.28. Solve: The electric potential at the dot is () 123 01 02 03 99 92 2 22 111 444 5.0 10 C 9.0 10 Nm /C 3140 V 0.040 m 0.020 m 0.020 m 0.040 m qqq V rrr q πε −− =++ ⎡⎤ −× × + + = ⎢⎥ + ⎣⎦ Solving yields q = 1.00 × 10 –8 C = 10.0 nC. Assess: Potential is a scalar quantity, so we found the net potential by adding three scalar quantities.

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29.30. Model: The net potential is the sum of the scalar potentials due to each charge. Visualize: Solve: Let the point on the y -axis where the electric potential is zero be at a distance y from the origin. At this point, V 1 + V 2 = 0 V. This means () 99 12 22 02 2 1 3.0 10 C 4.0 10 C 0 V 0 4 9.0 cm 16.0 cm qq rr yy πε −− ⎧⎫ −× × +=⇒ + = ⎨⎬ ⎩⎭ −+ + ( ) ( ) 2 2 3 16 cm 4 9 cm 9 256 cm 16 81 cm yyy y ⇒+ = + + = + 7 y 2 = 1008 cm 2 y = ± 12 cm.
29.42. Model: Energy is conserved. The potential energy is determined by the electric potential. Visualize: Please refer to Figure P29.42. Solve: The proton at point A is at a potential of 30 V and its speed is 50,000 m/s. At point B, the proton is at a potential of 10 V and we are asked to find its speed. Clearly, the proton moves into a lower potential region, so its speed will increase. The conservation of energy equation

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HW07solutions - 29.28 Model The electric potential at the...

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