1. Answer (a) through (c) for both Figures 1 and 2. +q d +q d -q +q d d d d +q +q -q d Figure 1 +q d Figure 2 a. Calculate the net electric field at the center of the squares. b. Calculate the net electric force on a positive $Q$ charge that is placed at the center of the squared. c. Compare the results from the two arrangements of charges.
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Step 1: The electric field at the center of the square due to each charge is given by Coulomb's law: $$E = \frac{kq}{r^2}$$ where k is Coulomb's constant, q is the charge, and r is the distance from the charge to the center of the square. Show more…
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1a. Four equal positive charges of magnitude + q are located at the corners of a square ABCD. (A and B are the upper left and right corners, and C and D are the lower left and right corners respectively.) Find the direction of the net force on charge qA. The side of the square is a. A. straight up B. straight down C. along the diagonal, toward the centre D. along the diagonal, away from the centre 1b. We would like to cancel the net force on each of the four corner charges, by placing a single new charge on the square. What kind of charge would it have to be? Where should you place the new (fifth charge)? A. positive, at the centre B. positive, at the midpoint of one of the sides C. negative, at the centre D. negative, at the midpoint of one of the sides
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Four point charges, each of magnitude $q$, are located at the corners of a square with sides of length $d$. Two of the charges are $+q$, and two are $-q$. The charges are arranged in one of the following two ways: (1) The charges alternate in sign $(+q,-q,+q,-q)$ around the square; $(2)$ the top two corners of the square have positive charges $(+q,+q)$, and the bottom two corners have negative charges $(-q,-q)$. (a) In which case will the electric field at the center of the square have the greater magnitude? Explain. (b) Calculate the electric field at the center of the square for each of these two cases. (Give your result as a multiple of $\mathrm{kq} / \mathrm{d}^{2}$.)
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