5. An Ensemble of Discrete PointLike Charges Consider the following arrangement of xed point-like charges. 29 a. Predict the resultant force that acts on the 5.00 110 as a result of the other two charges. Make this prediction by first drawing force vectors for the interaction between the charge at the origin and each of the other charges. Ensure that the force vectors you draw are to scale [e.g. if one force is greater than the other. the arrows you draw should reflect that}. Use head-to-tail vector addition to arrive at your prediction. No calculations are necessary to answer this question. only.r vector diagrams are needed. b. Calculate the magnitude of the force on the 5.00 110 due to each of the other charges. Explain your calculations. c. Find the resultant force that acts on the 5.00 :10 as a result of the other two charges and express your answer as a vector using the unit vectors i and 3'. Explain your work. d. Find the magnitude and direction of the force in part c. Explain your conclusions. 3. Coulomb's Law and Superposition Coulomb's law allows us to find the force between two point charges. Three point charges are held fixed in place as show below. +9 Consider the following comment about this situation: "There will be zero net electric force on the charge in the middle due to the other charges. Using Coulomb's law, the force due to the +Q charge is positive, and the force due to the -Q charge is negative. The forces cancel." a. Do you agree with this statement? Explain. b. How does Coulomb's law apply to situations in which there are more than two charges?4. Superposition and Discrete Charge Ensembles Each of the following parts involves a comparison of the net force exerted on a positive charge + q in two different cases. a. In cases A and B shown below, there are two positive point charges + @ each a distance s away from a third positive point charge + o 0+0 +g o Case A Case B Is the net electric force on the + q charge in case A greater than, less than, or equal to the net electric force on the +q charge In case B? Explain. b. In case C. two positive point charges +20 are each a distance s away from a third positive point charge +q. In case !), four positive point charges +@ are each a distance s away from a fifth positive point charge +q. (The angle c shown is the same in both cases.) 120 0+20 +0 Case C Case D Is the net electric force on the +q charge in case C' greater than, less than, or equal to the net electric force on the + g charge in case D? Explain. C. In case E , a positive point charge with + @ is a distance s away from a second positive point charge + q In case , ten positive point charges, each with charge +, . lie along an arc of radius & centered on a positive point charge +q- +0/10 0+0 Case E Case F Is the net electric force on the + q charge in case E greater than, less than, or equal to the net electric force on the + q charge in case F? Explain. +0 C. A thin semicircular rod has a total charge + @ uniformly distributed along it. A negative point charge -Q is placed as shown, A test charge +q is placed at point C. (Point ( is equidistant from -Q and from all points on the rod.)2. Three Dimensional Vectors Consider the following sketch of a three-dimensional vector V. Z 30 B F = 20.0 vector B = 5.0 D 530 | components projection - Vu VI D y D = 20.0 The vector, drawn as a blue arrow, has components V/2. by. and V2. Notice that not all the components are positive, and that if you add up all three components using head-to-tail addition, you arrive back at the original vector. Let's consider a more concrete example of a position vector measured in meters: R = (2 m)i + (1 m)j + (3 m)k. 370 a. Attempt to sketch it from a "perspective view" that shows all three dimensions simultaneously (like the above example]. This type of figure is intended to give the viewer a 3D impression of the vector using a 2D drawing. Sketching components also helps the viewer orient the vector in the 3D reference system. b. Attempt to sketch the vector from two different 2D perspectives, with either the z-axis pointing out of the page or the I-axis pointing out of the page. This type of figure gives the viewer a 20 projection of the vector on a single plane (e.g on the zy-plane or the yz-plane only). Examples of this perspective can be fou in problem 1 where the vectors were shown in the cy-plane, with the z-axis directed out of the page. Note that in 2D such projections are complete representations of the vector, but in 30, we lose information about one of the directions when employing such projections. c. Calculate the magnitude of R. d. Calculate the angle that R makes with the z-axis, y-axis, and z-axis le.g. one angle for each axis).1. Geometric Vector Manipulation For the vectors given in the figure below, use a graphical method (use ruler and protractor to earn full credit) to find the following resultants and double check your work using algebraic expressions for the vectors. A = 8.661 + 5.003, B = 3.014 + 3.993. C = 6.00i - 10.43, D = -16.01 + 12.0}, F = -17.31 -10.0} a. A + B b. C + B YA c. D - F X 60 d. C - 2D + 3F C = 12.0 A C A = 10.0 30 30 B F = 20.0 F B = 5.0 530