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1. Two alpha particles (helium nuclei), each consisting of two protons and two neutrons, have an electrical potential energy of 6.32 × 10-19 J. What is the distance between these particles at this time?
2. Two charges are located along the x-axis. One has a charge of 6.4 mC, and the second has a charge of -3.2 mC. If the electrical potential energy asso- ciated with the pair of charges is -4.1 × 10-2 J, what is the distance between the charges?
3. In a charging process, 1013 electrons are removed from a metal sphere and placed on a second sphere that is initially uncharged. Then the elec- trical potential energy associated with the two spheres is found to be -7.2 × 10-2 J. What is the distance between the two spheres?
4. A charge moves a distance of 2.0 cm in the direction of a uniform electric field having a magnitude of 215 N/C. The electrical potential energy of the charge decreases by 6.9 × 10-19 J as it moves. Find the magnitude of the charge on the moving particle. (Hint: The electrical potential energy depends on the distance moved in the direction of the field.)
A sphere of radius R is uniformly charged to a total charge of Q. It is made to spin about an axis that passes through its center with an angular speed ω. Find the magnitude of the resulting magnetic field at the center of the sphere.
A resistor is in the shape of a cube, with each side of resistance R . Find the equivalent resistance between any two of its adjacent corners.
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