Two point particles of charge Q₁ = 47 μC and Q₂ = 82 μC are found to have a potential energy of 45 J. What is the distance between the charges? m
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- (a) What voltage will accelerate electrons to a speed of 6.00107 m/s? (b) Find the radius of curvature of the path of a proton accelerated through this potential in a 0.500-T field and compare this with tire radius of curvature of an electron accelerated through the same potential.(a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength for air ( 3.0 106 V/m) if the plates are separated by 2.00 mm and a potential difference of 5.0 103 V is applied? (b) How close together can the plates be with this applied voltage?Four parallel metal plates P1, P2, P3, and P4, each of area 7.50 cm2, are separated successively by a distance d = 1.19 mm as shown in Figure P25.34. Plate P1 is connected to the negative terminal of a battery, and P2 is connected to the positive terminal. The battery maintains a potential difference of 12.0 V. (a) If P3 is connected to the negative terminal, what is the capacitance of the three-plate system P1P2P3? (b) What is the charge on P2? (c) If P4 is now connected to the positive terminal, what is the capacitance of the four-plate system P1P2P3P4? (d) What is the charge on P4?
- A Pairs of parallel wires or coaxial cables are two conductors separated by an insulator, so they have a capacitance. For a given cable, the capacitance is independent of the length if the cable is very long. A typical circuit model of a cable is shown in Figure P27.87. It is called a lumped-parameter model and represents how a unit length of the cable behaves. Find the equivalent capacitance of a. one unit length (Fig. P27.87A), b. two unit lengths (Fig. P27.87B), and c. an infinite number of unit lengths (Fig. P27.87C). Hint: For the infinite number of units, adding one more unit at the beginning does not change the equivalent capacitance.A wire having a uniform linear charge density is bent into the shape shown in Figure P24.27. Find the electric potential at point O. Figure P24.27In open-heart surgery, a much smaller amount of energy will defibrillate the heart, (a) What voltage is applied to the 8.00F capacitor of a heart defibrillator that stores 40.0 J of energy? (b) Find the amount of the stored charge.
- (a) Calculate the potential difference between points a and b in Figure P27.37 and (b) identify which point is at the higher potential. Figure P27.37The network of capacitors shown below are all uncharged when a 300-V potential is applied between points A and B with the switch S open, (a) What is the Potential difference VE-VD? (b) What is the potential at point E after the switch is closed? (c) How much charge flows through the switch after it is closed?A bare helium nucleus has two positive charges and a mass of 6.641027kg . (a) Calculate its kinetic energy in joules at 2.00% of the speed of light, (b) What is this in electron-volts? (c) What voltage would be needed to obtain this energy?
- A large parallel-plate capacitor is attached to a battery that has terminal potential (Fig. 27.15A). After a period of time, the capacitor stores charge Q so that its top plate is positive and its bottom plate is negative, and the potential difference between the plates is VC = . An I-shaped neutral conductor consisting of two parallel plates connected by a wire is slipped between the plates of the capacitor so that all four plates are parallel (Fig. 27.15B). What are the charges q1, and q2 on the plates of the I-shaped conductor? What is the potential difference VC between the top and bottom plates of the capacitor?(a) Will the electric field strength between two parallel conducting plates exceed the breakdown strength of dry air, which is 3.00106 V/m, if the plates are separated by 2.00 mm and a potential difference of 5.010V is applied? (b) How close together can the plates be with this applied voltage?A particle accelerator produces a beam with a radius of 1.25 mm with a current of 2.00 mA. Each proton has a kinetic energy of 10.00 MeV. (a) What is the velocity of the protons? (b) What is the number (n) of protons per unit volume? (b) How many electrons pass a cross sectional area each second?