Think Before You Compute!Consider the fixed arrangement of charges onthe hexagonal figure shown at right. All sidesare of equal length and all charges have amagnitude Q and are positive except #4 andthe center charge which are negative. Thedistance from the center to a corner is d.a. Draw a Free-Body diagram for thecenter charge showing all 6 forces.Label each with subscripts denotingthe interacting charges. For instance,64d132the force on the central charge from charge 3 is Fc3.Using a "brute force" method you would use this Free-Body diagram to find thevector sum of all 6 individual forces on the central charge without any clevernesslike making simplifications due to symmetry. Using a typical xy-coordinate systemwith x to the right and y up...b. Which forces (by name) need to be broken into components (i.e. they are notparallel to an axis)?c. How many distinct (non-zero) force-terms (i.e. either from forces orcomponents of forces) must be summed to find the net horizontal (✗) forceon the central charge? (Don't be clever, use brute force)d. How many distinct (non-zero) force-terms (i.e. either from forces orcomponents of forces) must be summed to find the net vertical (y) force onthe central charge? (Again, don't be clever)But if we are clever and consider symmetry before cranking through a problem wecan often simplify many things and can save ourselves work.e. In a set of concise sentences explain the simplifications that symmetry allowsyou to make about the magnitudes and direction of the forces.f. In as short a mathematical statement as possible (i.e. 1 term) write themagnitude of the net force on the central charge in terms of the electricconstant k, the charge Q, and the distance d. Give its direction as an angle upor down from the + or -x-axis.In the same way...g. What is the electric field at the center? Give magnitude and direction.h. What is the electric potential at the center?i. What is the electric potential energy of the charge at the center?

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Think Before You Compute! Consider the fixed arrangement of charges on the hexagonal figure shown at right. All sides are of equal length and all charges have a magnitude Q and are positive except #4 and the center charge which are negative. The distance from the center to a corner is d. a. Draw a Free-Body diagram for the center charge showing all 6 forces. Label each with subscripts denoting the interacting charges. For instance, 5 4 6 1 3 2 the force on the central charge from charge 3 is Fc3. Using a "brute force" method you would use this Free-Body diagram to find the vector sum of all 6 individual forces on the central charge without any cleverness like making simplifications due to symmetry. Using a typical xy-coordinate system with x to the right and y up... b. Which forces (by name) need to be broken into components (i.e. they are not parallel to an axis)? c. How many distinct (non-zero) force-terms (i.e. either from forces or components of forces) must be summed to find the net horizontal (x) force on the central charge? (Don't be clever, use brute force) d. How many distinct (non-zero) force-terms (i.e. either from forces or components of forces) must be summed to find the net vertical (y) force on the central charge? (Again, don't be clever) But if we are clever and consider symmetry before cranking through a problem we can often simplify many things and can save ourselves work. e. In a set of concise sentences explain the simplifications that symmetry allows you to make about the magnitudes and direction of the forces. f. In as short a mathematical statement as possible (i.e. 1 term) write the magnitude of the net force on the central charge in terms of the electric constant k, the charge Q, and the distance d. Give its direction as an angle up or down from the + or -x-axis. In the same way... g. What is the electric field at the center? Give magnitude and direction. h. What is the electric potential at the center? i. What is the electric potential energy of the charge at the center?

Think Before You Compute! Consider the fixed arrangement of charges on the hexagonal figure shown at right. All sides are of equal length and all charges have a magnitude Q and are positive except #4 and the center charge which are negative. The distance from the center to a corner is d. a. Draw a Free-Body diagram for the center charge showing all 6 forces. Label each with subscripts denoting the interacting charges. For instance, 5 4 6 1 3 2 the force on the central charge from charge 3 is Fc3. Using a "brute force" method you would use this Free-Body diagram to find the vector sum of all 6 individual forces on the central charge without any cleverness like making simplifications due to symmetry. Using a typical xy-coordinate system with x to the right and y up... b. Which forces (by name) need to be broken into components (i.e. they are not parallel to an axis)? c. How many distinct (non-zero) force-terms (i.e. either from forces or components of forces) must be summed to find the net horizontal (x) force on the central charge? (Don't be clever, use brute force) d. How many distinct (non-zero) force-terms (i.e. either from forces or components of forces) must be summed to find the net vertical (y) force on the central charge? (Again, don't be clever) But if we are clever and consider symmetry before cranking through a problem we can often simplify many things and can save ourselves work. e. In a set of concise sentences explain the simplifications that symmetry allows you to make about the magnitudes and direction of the forces. f. In as short a mathematical statement as possible (i.e. 1 term) write the magnitude of the net force on the central charge in terms of the electric constant k, the charge Q, and the distance d. Give its direction as an angle up or down from the + or -x-axis. In the same way... g. What is the electric field at the center? Give magnitude and direction. h. What is the electric potential at the center? i. What is the electric potential energy of the charge at the center?