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# Assign1 - PHY 54 Assignment 1 Summer 2011 Reading...

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Reading : Electrostatics 1. Key concepts: Electric charge, conservation of charge, Coulomb’s law, definition of E , force on charge in E-field, electric dipoles. 1. Calculations showing the strengths of the various fundamental forces. a. Two identical bodies of mass 1 kg and charge 1 C are 1 m apart. What is the ratio of the Coulomb repulsion to the gravitational attraction? b. Consider two protons in a nucleus, at distance 1 fm ( = 10 15 m) apart. What is the Coulomb force of repulsion between them? [This must be balanced by the “strong” force that binds the nucleus.] 2. Two positive point charges are a distance r apart. The total charge of the pair is Q . If each charge is Q /2, the force of repulsion is F 0 . a. Show that dividing the charge unequally gives a force smaller than F 0 . b. What are the two charges if the force is 3 4 F 0 ? 3. Two positive point charges of magnitude Q are held in place on the x -axis at x = 10 cm and x = 10 cm. A small bead carrying charge – q is threaded on a non- conducting fiber that runs along the y -axis, constraining the bead to move only along that axis. Initially the bead is at rest at y = 0 . a. Show that the origin is a point of stable equilibrium for the bead. That is, show that if the bead is displaced slightly the forces on it will bring it back toward the origin. (No calculation, only an argument based on directions.) b. Now suppose the fiber runs along the x -axis instead. Is the origin still a point of stable equilibrium for the bead? Explain. 4. Two point charges, q and Q , are separated by distance . We are interested in the total E-field at points on the line passing through the charges. a. If q and Q have the same sign, is there a point on that line between them where E = 0 ? If so, how far is it from q ?

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Assign1 - PHY 54 Assignment 1 Summer 2011 Reading...

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