1- A spherical capacitor is made from two thin concentric conducting shells. The inner shell has radius r1, and the outer shell has radius r2. What is the fractional difference in the capacitances of this spherical capacitor and a parallel plate capacitor made from plates that have the same area as the inner sphere and the same separation d = r2 - r1 between plates? (Use the following as necessary: r1, r2, and ε0.)
2- Four capacitors with capacitances C1 = 3.4 nF, C2 = 2.2 nF, C3 = 1.6 nF, and C4 = 5.3 nF are wired to a battery with V = 10.3 V, as shown in the figure. What is the equivalent capacitance of this set of capacitors?
3- A potential difference of V = 80.0 V is applied across a circuit with capacitances C1 = 14.5 nF, C2 = 4.00 nF, and C3= 26.5 nF, as shown in the figure. What is the magnitude and sign of q3l, the charge on the left plate of C3 (marked by point A)? What is the electric potential, V3, across C3? What is the magnitude and sign of the charge q2r, on the right plate of C2 (marked by point B)?
4- Fifty-two parallel plate capacitors are connected in series. The distance between the plates is d for the first capacitor, 2d for the second capacitor, 3d for the third capacitor, and so on. The area of the plates is the same for all the capacitors. Express the equivalent capacitance of the whole set in terms of C1 (the capacitance of the first capacitor).
5- A 7000-nF parallel plate capacitor is connected to a 2.4-V battery and charged. (a) What is the charge Q on the positive plate of the capacitor? (b) What is the electric potential energy stored in the capacitor? The 7000-nF capacitor is then disconnected from the 2.4-V battery and used to charge three uncharged capacitors, a 100-nF capacitor, a 200-nF capacitor, and a 300-nF capacitor, connected in series. (c) After charging, what is the potential difference across each of the four capacitors? d) How much of the electrical energy stored in the 7000-nF capacitor was transferred to the other three capacitors?
24.48. The Earth is held together by its own gravity. But it is also a charge-bearing conductor. (a) The Earth can be regarded as a conducting sphere of radius 6371 km, with electric field E = (-150. V/m) at its surface, where is a unit vector directed radially outward. Calculate the total electrostatic potential energy associated with the Earth's electric charge and field. (b) The Earth has gravitational potential energy, akin to the electrostatic potential energy. Calculate this energy, treating the Earth as a uniform solid sphere.(Hint: dU = -(GM/r)dM. The mass of the Earth is 5.97 1024 kg. Assume that the density of the Earth is uniform.) (c) Use the results of parts (a) and (b) to address this question: To what extent do electrostatic forces affect the structure of the Earth?
6- A 2.1-nF parallel plate capacitor with a sheet of Mylar (κ = 3.1) filling the space between the plates is charged to a potential difference of 150 V and is then disconnected. (The initial capacitance including the dielectric is 2.1 nF.) (a) How much work is required to completely remove the sheet of Mylar from the space between the two plates? (b) What is the potential difference between the plates of the capacitor once the Mylar is completely removed?
7- A proton traveling along the x-axis at a speed of 5.0 * 106 m/s enters the gap between the plates of a 4.0-cm-wide parallel plate capacitor. The surface charge distributions on the plates are given by σ = ±1.0* 10-6 C/m2. How far has the proton been deflected sideways (Δy) when it reaches the far edge of the capacitor? Assume that the electric field is uniform inside the capacitor and zero outside. (The plates of the capacitor are parallel to the x-axis. The charge of the proton is +1.602 * 10-19 C and the mass of the proton is 1.67 *10-27 kg.)