Unit 10 Problem Set 10.1 Calculate the magnitude and direction of the Coulomb force on each of the three charges in the figure below. 10.2 Three charges are arranged as shown in the figure below. Find the magnitude and direction of the electrostatic force on the charge at the origin. 10.3 Three charges are arranged as shown in the figure below. Find the magnitude and direction of the electrostatic force on the 6.00-nC charge. 10.4 Three point charges are located at the corners of an equilateral triangle as in the figure below. Calculate the net electric force on the 7.00-μC charge. 10.5 Positive charges are situated at three corners of a rectangle, as shown in the figure below. Find the electric field at the fourth corner. 10.6 Three identical charges (q = –5.0 μC) are along a circle of 2.0-m radius at angles of 30°, 150°, and 270°, as shown in the figure below. What is the resultant electric field at the center of the circle? 10.7 (a) Sketch the electric field pattern around two positive point charges of magnitude 1 μC placed close together. (b) Sketch the electric field pattern around two negative point charges of –2 μC placed close together. (c) Sketch the pattern around two point charges of +1 μC and –2 μC placed close together. 10.8 Two point charges are a small distance apart. (a) Sketch the electric field lines for the two if one has a charge four times that of the other and both charges are positive. (b) Repeat for the case in which both charges are negative. 10.9 A 4.00-kg block carrying a charge Q = 50.0 μC is connected to a spring for which k = 100 N/m. The block lies on a frictionless horizontal track, and the system is immersed in a uniform electric field of magnitude E = 5.00 × 105 V/m directed as in Figure P16.9. (a) If the block is released at rest when the spring is unstretched (at x = 0), by what maximum amount does the spring expand? (b) What is the equilibrium position of the block? 10.10 The three charges in the figure below are at the vertices of an isosceles triangle. Calculate the electric potential at the midpoint of the base, taking q = 7.00 nC. 10.11 A small object with a mass of 350 mg carries a charge of 30.0 nC and is suspended by a thread between the vertical plates of a parallel-plate capacitor. The plates are separated by 4.00 cm. If the thread makes an angle of 15.0° with the vertical, what is the potential difference between the plates? 10.12 Find the charge on each of the capacitors below. 10.13 Find the equivalent capacitance between points a and b for the group of capacitors connected as shown below if C1 = 5.00 μF, C2 = 10.0 μF, and C3 = 2.00 μF. 10.14 Find the equivalent capacitance between points a and b in the combination of capacitors shown in Figure P16.42. 10.15 Two capacitors C1 = 25.0 μF and C2 = 5.00 μF are connected in parallel and charged with a 100-V power supply. (a) Calculate the total energy stored in the two capacitors. (b) What potential difference would be required across the same two capacitors connected in series in order that the combination store the same energy as in (a)? 10.16 A certain storm cloud has a potential difference of 1.00 × 108 V relative to a tree. If, during a lightning storm, 50.0 C of charge is transferred through this potential difference and 1.00% of the energy is absorbed by the tree, how much water (sap in the tree) initially at 30.0°C can be boiled away? Water has a specific heat of 4 186 J/kg · °C, a boiling point of 100°C, and a heat of vaporization of 2.26 × 106 J/kg.
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