Physics 11 Chapter 18: Electric Forces and Electric Fields

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1 Physics 11 Chapter 18: Electric Forces and Electric Fields Yesterday is not ours to recover, but tomorrow is ours to win or lose. Lyndon B. Johnson When I am anxious it is because I am living in the future. When I am depressed it is because I am living in the past. Anonymous Everyday is a good day; some are just better than others. Author unknown Reading: pages (skip capacitors); Outline: electric charge structure of the atom (PowerPoint) types of charge conservation of charge conductors and insulators (PowerPoint) ways of charging an object (PowerPoint) lightning (PowerPoint) Coulomb s law force between two point charges force on a point charge from more than one charge electric field definition electric field from point charges electric field lines (PowerPoint) electric shielding (PowerPoint) Problem Solving Many problems in this chapter deal with Coulomb's law. Given two charges and their separation, you should be able to calculate the force (both magnitude and direction) each exerts on the other. You should know how to use vector addition to find the resultant force when more than one charge interacts with the charge of interest. Variations include problems that ask you to find one of the charges or the position of a charge, given the force. To find the value of one or more of the charges in some problems, a preliminary calculation must be performed prior to using Coulomb's law. For example, you may need to calculate the total charge in an object. Remember that charge is quantized and can only occur in multiples of e = C.

2 You should know how to compute the electric field of a collection of point charges. Remember that the sum of the individual fields is a vector sum. Add the x components to get the x component of the sum; add the y components to get the y component of the sum. The magnitude of the electric field produced by a single point charge q, at a point a distance r away, is given by E = k q /r 2. This must be multiplied by the sine or cosine of an angle to obtain a component. You must also determine the sign of the component. Some problems deal with electric field lines. You should know that the electric field at any point is tangent to the line through that point, that the number of lines per unit area passing through an area perpendicular to the lines is proportional to the magnitude of the field, and that lines emanate from positive charge and end at negative charge. You will also need to know that the magnitude of the force on a charge in an electric field is given by the product of the charge and the electric field: F = qe. For a positive charge, the force is in the same direction of the electric field, while for a negative charge, it is in the opposite direction of the electric field. Questions and Example Problems from Chapter 18 Question 1 The figure below shows four situations in which charged particles are fixed in place on an axis. In which situation(s) is there a point to the left of the particle where an electron will be in equilibrium? Question 2 The figure to the right shows four situations in which particles of charge +q or q are fixed in place. In each, the particles on the x-axis are equidistant from the y-axis. What is the direction of the net force on the middle particle in each case?

3 Question 3 Drawings I and II show two examples of electric field lines. Decide which of the following statements are true and which are false, defending your choice in each case. (a) In both I and II the electric field is the same everywhere. (b) As you move from left to right in each case, the electric field becomes stronger. (c) The electric field in I is the same everywhere but becomes stronger in II as you move from left to right. (d) The electric fields in both I and II could be created by negative charges located somewhere on the left and positive charges somewhere on the right. (e) Both I and II arise from a single positive point charge located somewhere on the left. Problem 1 A plate carries a charge of 3.0 µc, while a rod carries a charge of +2.0 µc. How many electrons must be transferred from the plate to the rod, so that both objects have the same charge? Problem 2 The nucleus of the helium atom contains two protons that are separated by about m. Find the magnitude of the electrostatic force that each proton exerts on the other. (The protons remain together in the nucleus because the repulsive electrostatic force is balanced by an attractive force called the strong nuclear force.)

4 Problem 3 Two very small spheres are initially neutral and separated by a distance of 0.50 m. Suppose that 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? Problem 4 A charge of 3.00 µc is fixed at the center of a compass. Two additional charges are fixed on the circle of a compass (radius = m). The charges on the circle are 4.00 µc at the position due north and µc at the position due east. What is the magnitude and direction of the net electrostatic force acting on the charge at the center? Specify the direction relative to due east.

5 Problem 5 Given that q = +12 µc and d = 16 cm, find the direction and magnitude of the net electrostatic force exerted on charge q 1 in the figure below. Problem 6 A charge of C is located at a place where there is an electric field that points due east and has a magnitude of N/C. What are the magnitude and direction of the force acting on the charge? Problem 7 A tiny ball (mass = kg) carries a charge of 18 µc. What electric field (magnitude and direction) is needed to cause the ball to float above the ground?

6 Problem 8 Four point charges that have the same magnitude of C 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. Problem 9 Two charges, -16 µc and +4.0 µc, are fixed in place and separated by 3.0 m. (a) At what spot along a line through the charges is the net electric field zero? Locate this spot relative to the positive charge. (b) What would be the force on a charge of +14 µc placed at this spot?

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