Note: Each of these problems consists of Concept Questions followed by a related quantitative Problem. They are designed for use by students working alone or in small learning groups. The Concept Questions involve little or no mathematics and are intended to stimulate group discussions. They focus on the concepts with which the problems deal. Recognizing the concepts is the essential initial step in any problem-solving technique.

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Concept Questions Two identical metal spheres have charges of q_{1} and q_{2}. They are brought together so they touch, and then they are separated. (a) How is the net charge on the two spheres before they touch related to the net charge after they touch? (b) After they touch and are separated, is the charge on each sphere the same? Why?

Problem Four identical metal spheres have charges of q_{A}=–8.0 mC, q_{B}=–2.0 mC, q_{C}=+5.0 mC, and q_{D}=+12.0 mC. (a) Two of the spheres are brought together so they touch and then they are separated. Which spheres are they, if the final charge on each of the two is +5.0 mC? (b) In a similar manner, which three spheres are brought together and then separated, if the final charge on each of the three is +3.0 mC? (c) How many electrons would have to be added to one of the spheres in part (b) to make it electrically neutral?

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Concept Questions The drawings show three charges that have the same magnitude, but different signs. In all cases the distance between charges 1 and 2 and between 2 and 3 is the same. (a) Draw the electrical force that each charge exerts on charge 2. Each force should be drawn in the correct direction, and its magnitude should be correct relative to that of the other force. (b) Rank the magnitudes of the net electrical force on charge 2, largest first. Explain.

Problem The magnitude of the charges is q=8.6 mC, and the distance between them is 3.8 mm. Determine the magnitude of the net force on charge 2 for each of the three drawings. Verify that your answers are consistent with your answers to the Concept Questions.

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Concept Questions Suppose you want to neutralize the gravitational attraction between the earth and the moon by placing equal amounts of charge on each. (a) Should the charges be both positive, both negative, or one positive and the other negative? Why? (b) Do you need to know the distance between the earth and the moon to find the magnitude of the charge? Why or why not?

Problem The masses of the earth and moon are 5.98×10^{24} and 7.35×10^{22} kg, respectively. Identical amounts of charge are placed on each body, such that the net force (gravitational plus electrical) on each is zero. What is the magnitude of the charge?

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Concept Questions Suppose you want to determine the electric field in a certain region of space. You have a small object of known charge and an instrument that measures the magnitude and direction of the force exerted on the object by the electric field. How would you determine the magnitude and direction of the electric field if the object were (a) positively charged and (b) negatively charged?

Problem(a) The object has a charge of +20.0 mC and the instrument indicates that the electric force exerted on it is 40.0 mN, due east. What is the magnitude and direction of the electric field? (b) What is the magnitude and direction of the electric field if the object has a charge of –10.0 mC and the instrument indicates that the force is 20.0 mN due west?

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Concept Questions The drawing shows two situations in which charges are placed on the x and y axes. They are all located at the same distance from the origin. Without doing any calculations, does the electric field at the origin in part (a) have a magnitude that is greater than, less than, or equal to the magnitude of the field at the origin in part (b)? Justify your answer.

Problem The distance between each of the charges and the origin is 6.1 cm. For each of the situations shown in the drawing, determine the magnitude of the electric field at the origin. Check to see that your results are consistent with your answer to the Concept Question.

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Concept Questions A proton and an electron are moving due east in a constant electric field that also points due east. (a) Does each experience an electric force of the same magnitude and direction? (b) What is the direction of the proton’s acceleration and the direction of the electron’s acceleration? (c) Is the magnitude of the proton’s acceleration greater than, less than, or the same as that of the electron’s acceleration? Explain your answers.

Problem The electric field points due east and has a magnitude of 8.0×10^{4} N/C. Determine the magnitude of the acceleration of the proton and the electron. Check that your answers are consistent with part (c) of the Concept Questions.

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Concept Questions Three point charges have equal magnitudes, two being positive and one negative. These charges are fixed to the corners of an equilateral triangle, as the drawing shows. (a) The charge at any one corner experiences forces from the charges at the other corners. Do the individual forces exerted by the charges have the same or different magnitudes? (b) At which one or more corners does (do) the charge(s) experience a net force that has the greatest magnitude? (c) At which one or more corners does (do) the charge(s) experience a net force that has the smallest magnitude?

Problem The magnitude of each of the charges is 5.0 mC, and the lengths of the sides of the triangle are 3.0 cm. Calculate the magnitude of the net force that each charge experiences. Be sure that your answers are consistent with your answers to the Concept Questions.

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Concept Questions The drawing shows a positive point charge +q_{1}, a second point charge q_{2} that may be positive or negative, and a spot labeled P, all on the same straight line. The distance d between the two charges is the same as the distance between q_{1} and the point P. With q_{2} present, the magnitude of the net electric field at P is twice what it is when q_{1} is present alone. (a) When the second charge is positive, is its magnitude smaller than, equal to, or greater than the magnitude of q_{1}? Explain your reasoning. (b) When the second charge is negative, is its magnitude smaller than, equal to, or greater than that in question (a)? Account for your answer.

Problem Given that q_{1}=+0.50 mC, determine q_{2} when it is (a) positive and (b) negative. Verify that your answers are consistent with your answers to the Concept Questions.