JiTT Exercises

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1			The following hypothetical reaction shows a neutron (n) decaying into a proton (p⁺) and an electron (e^-): n → p⁺ + e^- At first there is no charge, but then charge seems to be "created." Does this reaction violate the law of charge conservation? Explain. (In Section 29.3 it is shown that the neutron does not decay into just a proton and an electron; the decay products include a third, electrically neutral particle.)




2			Explain why electric field lines never cross.




3			An electroscope consists of a conducting sphere, conducting pole, and two metal foils (Fig. 16.7a). The electroscope is initially uncharged. (a) A positively charged rod is allowed to touch the conducting sphere and then is removed. What happens to the foils and what is their charge? (b) Next, another positively charged rod is brought near to the conducting sphere without touching it. What happens? (c) The positively charged rod is removed and a negatively charged rod is brought near the sphere. What happens? Fig. 16.7a




4			A negatively charged rod is brought near a grounded conductor. After the ground connection is broken, the rod is removed. Is the charge on the conductor positive, negative, or zero? Explain.




5			Suppose a 1.0-g nugget of pure gold has zero net charge. What would be its net charge after it has 1.0% of its electrons removed?




6			If the electrical force of repulsion between two 1 C charges is 10 N, how far apart are they?




7			A K⁺ ion and a Cl^- ion are directly across from each other on opposite sides of a membrane 9.0 nm thick. What is the electric force on the K⁺ ion due to the Cl^- ion? Ignore the presence of other charges.




8			A small sphere with a charge of -6.0 × 10^-7 C is placed in a uniform electric field of magnitude 1.2 × 10⁶ N/C pointing to the west. What is the magnitude and direction of the force on the sphere due to the electric field?




9			What are the magnitude and direction of the acceleration of an electron at a point where the electric field has magnitude 6100 N/C and is directed due north?




10			An electron traveling horizontally from west to east enters a region where a uniform electric field is directed upward. What is the direction of the electric force exerted on the electron once it has entered the field?




11			(a) Find the electric flux through each side of a cube of edge length a in a uniform electric field of magnitude E. The field direction is perpendicular to two of the faces. (b) What is the total flux through the cube?




12			A raindrop inside a thundercloud has charge -8e. What is the electric force on the raindrop if the electric field at its location (due to other charges in the cloud) has magnitude 2.0 × 10⁶ N/C and is directed up?




13			In a thunderstorm, charge is separated through a complicated mechanism that is ultimately powered by the Sun. A simplified model of the charge in a thundercloud represents the positive charge accumulated at the top and the negative charge at the bottom as a pair of point charges (Fig. 16.51). (a) What is the magnitude and direction of the electric field produced by the two point charges at point P, which is just above the surface of the Earth? (b) Thinking of the Earth as a conductor, what sign of charge would accumulate on the surface near point P? (This accumulated charge increases the magnitude of the electric field near point P.) Fig. 16.51

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