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Question
(a) Find the electric field at $x = 5.00\textrm{ cm}$ in Figure 18.51(a), given that $q = 1.00\textrm{ }\mu\textrm{C}$. (b) At what position between 3.00 and 8.00 cm is the total electric field the same as that for $-2q$ alone? (c) Can the electric field be zero anywhere between 0.00 and 8.00 cm? (d) At very large positive or negative values of x, the electric field approaches zero in both (a) and (b). In which does it most rapidly approach zero and why? (e) At what position to the right of 11.0 cm is the total electric field zero, other than at infinity? (Hint: A graphing calculator can yield considerable insight in this problem.)
1. $4.00\times 10^{7}\textrm{ N/C}$
2. At $x = 7.00\textrm{ cm}$ the fields from both $+q$ charges will cancel, leaving the net electric field the same as that of the $-2q$ charge alone.
3. No, the electric field does not become zero between $x = 0.00 \textrm{ cm}$ and $x = 8.00\textrm{ cm}$
4. At large distances the electric field approaches that of a point net charge. The net charge in part (a) of the figure is zero, so it approaches zero more rapidly than in part (b), since part (b) has a net charge of $+q$
5. The electric field is zero at $30.60\textrm{ cm}$

Solution Video

# OpenStax College Physics for AP® Courses Solution, Chapter 18, Problem 16 (Problems & Exercises) (17:25)  