Two point charges are 2.00 m apart as shown on the right. The charge of the first object is -1.50 C, while the second object has a charge of +6.85 C. At which point will the electric field vector be zero?

Question

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Answer 1

To find the point at which the electric field vector is zero, we can use the principle of superposition. The electric field at a point due to both charges is the vector sum of the electric fields due to each charge separately.

Let's assume that the positive charge (+6.85 C) is located at point A, and the negative charge (-1.50 C) is located at point B. We want to find the point at which the electric field is zero.

Since the electric field due to a point charge is directed radially outward for a positive charge and radially inward for a negative charge, the electric field at point A due to the positive charge is directed away from point A and the electric field at point A due to the negative charge is directed towards point A.

At a point between A and B, the electric field at that point due to the positive charge will be stronger than the electric field due to the negative charge because the positive charge is bigger in magnitude. Therefore, the net electric field at that point will be directed away from point A.

At a point beyond B, the electric field at that point due to the negative charge will be stronger than the electric field due to the positive charge because the negative charge is closer to that point. Therefore, the net electric field at that point will be directed towards point A.

Therefore, if we move from point A towards point B, there must be a point where the electric field changes direction from away to towards point A. This is the point where the electric field is zero.

Therefore, the electric field vector will be zero at a point somewhere between the two charges, closer to the negative charge (-1.50 C).

Note: The specific location of the point at which the electric field is zero can be found by setting up an equation using Coulomb's law and solving for the distance from the negative charge (-1.50 C). However, no specific distances or coordinates are provided in the question, so we can only determine that the point will be between the two charges.