Physics Problem, please help?

Question

Two charges, -13 and +4.8 µC, are fixed in place and separated by 2.3 m. (a) At what spot along a line through the charges is the net electric field zero? Give the distance of the spot to the positive charge in meters (m). (Hint: The spot does not necessarily lie between the two charges.) (b) What would be the force on a charge of +14 µC placed at this spot?

Answer 1

The net electric field is equal to the net force per charge. So answering b) is easy; where the net electric field is zero, the force felt by any charge is also zero.

As for a), the electric field due to a point charge is directly proportional to the charge and inversely proportional to the distance from the charge. The electric field due to a negative charge points towards the charge, and the electric field due to a positive charge points away. Assume that the -13 µC charge is located at position x = 0 and the +4.8 µC charge is located at a position of x = 2.3 m. Now, anywhere between the two charges (0 < x < 2.3), the net electric field always points towards the -13 µC charge, which is also away from the +4.8 µC charge. So the charge cannot be zero there. And since the -13 µC charge is larger in magnitude than the +4.8 µC charge, at any point x < 0, the electric field will point in the negative direction because these points are also closer to the -13 µC charge than to the +4.8 µC charge. So our unknown position must be x > 2.3 m. Such a point is a distance of x from the -13 µC charge and a distance of x + 2.3 from the +4.8 µC charge. Thus, by Coulomb's law, the electric field at x is proportional to (-13/x^2) + (4.8/(x + 2.3)^2). Set this equal to zero and use algebra to solve. Here's a hint: Move the first term to the opposite side of the equation and use cross-multiplication.

Answer 2

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