1. Two spheres, each of mass M=2.33 g, are attached to pieces of string of length L=45 cm to a common point. The strings initially hang straight down, with the spheres just touching one another. An equal amount of charge, q , is placed on each sphere. The resulting forces on the spheres cause each string to hang at an angle of Ɵ=10 ͦ from the vertical. Determine q, the amount of charge on each sphere.
2. A 2-kW heater element from a dryer has a length of 80 cm. If a 10 cm section is removed, what power is used by the now shortened element at 120 V?
3. A conducting solid sphere of radius 20 cm is located with its center at the origin of a three-dimensional coordinate system. A charge of 0.271 nC is placed on the sphere.
(a) What is the magnitude of the electric field at point (x, y, z)=(23.1 cm, 1.1 cm, 0 cm)?
(b) What is the angle of this electric field with the x-axis at this point?
(c) What is the magnitude of the electric field at point (x, y, z)=(4.1 cm, 1.1 cm, 0 cm) ?
4. Two parallel plates are held at potentials of +200 V and -100 V. The plates are separated by 1 cm.
(a) Find the electric field between the plates.
(b) An electron is initially placed midway between the plates. Find its kinetic energy when it hits the positive plate.
5. A point charge of +2 μC is located at (2.5 m, 3.2 m). A second point charge of -3.1 μC is located at (-2.1 m, 1 m).
(a) What is the combined electrostatic potential of this two charges at x=20.1 cm, also on the x-axis?
(b) At which point(s) on the x-axis does this potential have minimum?
6. A 5-nF capacitor charged to 60 V and a 7-nF capacitor charged to 40 V are connected with the negative plate of each connected with the negative plate of the other. What is the final charge on the 7-nF capacitor?
7. A current density of 6×10-13 A/m2 exists in the atmosphere at a location where the electric field is 100 V/m. Calculate the electric conductivity of the Earth’s atmosphere in this region
8. When a 40-V emf device is placed across two resistors in series, a current of 10 A is flowing in each of the resistors. When the same emf device is placed across the same two resistors in parallel, the current through the emf device is 50 A. What is the magnitude of the larger of the two resistors?
9. A parallel-plate capacitor is charged and then disconnected from a battery. By what factor does the stored energy change ( increase or decrease) when the plate separation is doubled ?
10. A small but measurable current of 1.2×10-10 A exists in a copper wire whose diameter is 2.5 mm. The number of charge carriers per unit volume is 8.49 x1028 m-3. Assuming the current is uniform, calculate (a) the current density and (b) electron drift speed.