Concept explainers
Two particles, with charges of 20.0 nC and –20.0 nC, are placed at the points with coordinates (0, 4.00 cm) and (0, –4.00 cm) as shown in Figure P20.19. A particle with charge 10.0 nC is located at the origin. (a) Find the electric potential energy of the configuration of the three fixed charges. (b) A fourth particle, with a mass of 2.00 × 10–13 kg and a charge of 40.0 nC, is released from rest at the point (3.00 cm, 0). Find its speed after it has moved freely to a very large distance away.
(a)
The electric potential energy.
Answer to Problem 19P
The electric potential energy is
Explanation of Solution
Write the equation for the net potential energy.
Here,
Write the expression for potential energy to bring 20nC charge.
Here,
Write the expression for the potential.
Here,
Write the expression for potential energy to bring -20nC charge.
Here,
Write the expression for the potential.
Here,
Rewrite the expression from (I) by using (II), (III) (IV), (V).
Conclusion:
Substitute,
Thus, the electric potential energy is
(b)
The speed of the third object.
Answer to Problem 19P
The speed of the third object is
Explanation of Solution
Write the equation from conservation of energy.
Here,
Write the expression for the net potential.
Write the expression for potential.
Here,
Rewrite the expression from (VII) by using (III), (V), (VIII) and (IX).
Conclusion:
Substitute,
Thus, the speed of the third object is
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Chapter 20 Solutions
Principles of Physics
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