Question

Consider the electric field at the three points indicated by the letters A, B, and C in Fig. 16–49. First draw an arrow at each point indicating the direction of the net force that a positive test charge would experience if placed at that point, then list the letters in order of decreasing field strength (strongest first). Explain.

Short answer

The net electric force at points A and B is repulsive and at point C, it is zero. Electric field strength is the strongest at point A and weakest at point C such that letters in order of their decreasing field strength can be written as: \({\rm{A}} > {\rm{B}} > {\rm{C}}\)

Step-by-step solution

Understanding the electric field lines

The electric field line denotes a path that can be curved as well as straight along which a unit positive test charge would move if it is free to do so.

The tangent to the electric field line at any point gives the direction of the electric field at that point, whereas the density of electric field lines denotes the magnitude of the electric field.

Determination of the direction of net force at points A, B and C

If a positive test charge is placed at point A, then the force experienced by this test charge due to both the positive charges would be repulsive. Therefore, the direction of the net force experienced by the test charge would be away from the positive charge. Thus, the direction of net force would be pointed towards the left of the charge and parallel to its nearby electric field lines, as shown in the figure below:

If a positive test charge is placed at point B, then the force experienced by this test charge due to both the positive charges would be repulsive. Therefore, the direction of the net force experienced by this test charge would be pointed towards the right of the charge and parallel to its nearby electric field lines, as shown in the figure above.

If a positive test charge is placed at point C, then the force experienced by this test charge would be zero due to both the positive charges. This is because both the charges are placed equidistant from point C, and therefore the force experienced by the test charge would be equal and opposite. Thus, net force would be equal to zero.

Determination of the order of decreasing field strength

Since point A is much closer to the positive charge around which the density of electric field lines is much more as compared to point B. Thus the net electric field strength on point A would be much greater than at point B. However, the electric field strength at point C would be zero.

Thus, letters can be arranged in the order of their decreasing field strengths as:

\({\rm{A}} > {\rm{B}} > {\rm{C}}\)