What is the charge?

Look at the drawing of the electric field in Figure 18.20. What is the relative strength and sign of the three charges?

Figure 18.20 Map of electric field due to three charged particles.

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Strategy
We know the electric field extends out from positive charge and terminates on negative charge. We also know that the number of electric field lines that touch a charge is proportional to the charge. Charge 1 has 12 fields coming out of it. Charge 2 has six field lines going into it. Charge 3 has 12 field lines going into it.
Solution
The electric-field lines come out of charge 1, so it is a positive charge. The electric-field lines go into charges 2 and 3, so they are negative charges. The ratio of the charges is $q_{1} : q_{2} : q_{3} = + 12 : - 6 : - 12$ . Thus, magnitude of charges 1 and 3 is twice that of charge 2.

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