a.
The diagram show the three posibilities to locate the third charge (positions A, B or C). At position A, electric force between charges 1 and 3 is repulsive, then it goes to the left, while force between charges 2 and 3 is atractive, so it goes to the right. A similar behavior is observed at position C. Only in position B net electric force is not 0. Then, only at position A or C it could be possible to get a net electric force equal to 0.
b.
To find the place to put the third charge, we have to consider static equilibrium. Then:
Defining x as the distance from charge of 4 micro Coulombs (q1) to the third charge, then, for option A:
Since x is defined as a magnitude, then should be positive. Then:
And, for option C:
Again, x is defined as a magnitude, then:
This result is lesser than 5, then it is not possible to locate the third charge in position C (where x should be greather than 5m).
Conclusion. The only one position where net electric force is 0 for the third charge is at 12.071m to the left of charge of 4 micro Coulombs (position A).
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