Additional Problems

	55

Concept Simulation 18.2 provides background concerning the electric field lines that are the focus of this problem. Review the important features of electric field lines discussed in Conceptual Example 12. Three point charges (+q, +2q, and –3q) are at the corners of an equilateral triangle. Sketch in six electric field lines between the three charges.

Answer

	56

Two very small spheres are initially neutral and separated by a distance of 0.50 m. Suppose that 3.0×10¹³ electrons are removed from one sphere and placed on the other. (a) What is the magnitude of the electrostatic force that acts on each sphere? (b) Is the force attractive or repulsive? Why?

	SSM
	Example 2

	57

Conceptual Example 13 deals with the hollow spherical conductor in Figure 18.31. The conductor is initially electrically neutral, and then a charge +q is placed at the center of the hollow space. Suppose the conductor initially has a net charge of +2q instead of being neutral. What is the total charge on the interior and on the exterior surface when the +q charge is placed at the center?

Answer

	58

Four point charges have the same magnitude of 2.4×10^–12 C and are fixed to the corners of a square that is 4.0 cm on a side. Three of the charges are positive and one is negative. Determine the magnitude of the net electric field that exists at the center of the square.

	59

A charge of +3.0×10^–5 C is located at a place where there is an electric field that points due east and has a magnitude of 15 000 N/C. What are the magnitude and direction of the force acting on the charge?

	Answer
	SSM
	Example 7

	60

A charge +q is located at the origin, while an identical charge is located on the x axis at x=+0.50 m. A third charge of +2 q is located on the x axis at such a place that the net electrostatic force on the charge at the origin doubles, its direction remaining unchanged. Where should the third charge be located?

Example 4

	61

Consult Concept Simulation 18.1 for insight into this problem. Three charges are fixed to an x, y coordinate system. A charge of +18 mC is on the y axis at y=+3.0 m. A charge of –12 mC is at the origin. Last, a charge of +45 mC is on the x axis at x=+3.0 m. Determine the magnitude and direction of the net electrostatic force on the charge at x=+3.0 m. Specify the direction relative to the –x axis.

	Answer
	SSM
	Example 5

	62

A long, thin rod (length=4.0 m) lies along the x axis, with its midpoint at the origin. In a vacuum, a +8.0 mC point charge is fixed to one end of the rod, and a –8.0 mC point charge is fixed to the other end. Everywhere in the x, y plane there is a constant external electric field (magnitude=5.0×10³ N/C) that is perpendicular to the rod. With respect to the z axis, find the magnitude of the net torque applied to the rod.

	63	*

Two charges are placed between the plates of a parallel plate capacitor. One charge is +q₁ and the other is q₂=+5.00 mC. The charge per unit area on each plate has a magnitude of s=1.30×10^–4 C/m². The force on q₁ due to q₂ equals the force on q₁ due to the electric field of the parallel plate capacitor. What is the distance r between the two charges?

Answer

	64	*

Two small charged objects are attached to a horizontal spring, one at each end. The magnitudes of the charges are equal, and the spring constant is 220 N/m. The spring is observed to be stretched by 0.020 m relative to its unstrained length of 0.32 m. Determine (a) the possible algebraic signs and (b) the magnitude of the charges.

	65	*

Interactive Solution 18.65 provides a model for problems of this kind. A small object has a mass of 3.0×10^–3 kg and a charge of –34 mC. It is placed at a certain spot where there is an electric field. When released, the object experiences an acceleration of 2.5×10³ m/s² in the direction of the +x axis. Determine the magnitude and direction of the electric field.

Answer

	66	*

A small object, which has a charge q=7.5 mC and mass m=9.0×10^–5 kg, is placed in a constant electric field. Starting from rest, the object accelerates to a speed of 2.0×10³ m/s in a time of 0.96 s. Determine the magnitude of the electric field.

	67	*

Two spheres are mounted on identical horizontal springs and rest on a frictionless table, as in the drawing. When the spheres are uncharged, the spacing between them is 0.0500 m, and the springs are unstrained. When each sphere has a charge of +1.60 mC, the spacing doubles. Assuming that the spheres have a negligible diameter, determine the spring constant of the springs.

	Hint
	Answer
	SSM

	68	**

Two identical small insulating balls are suspended by separate 0.25-m threads that are attached to a common point on the ceiling. Each ball has a mass of 8.0×10^–4 kg. Initially the balls are uncharged and hang straight down. They are then given identical positive charges and, as a result, spread apart with an angle of 36° between the threads. Determine (a) the charge on each ball and (b) the tension in the threads.