Hello. The first image is the question, the second image is from the solutions manual. I don't understand why these answers are negative. Anyone have a clue?
Sure. (and Welcome to the PF)cros0 said:
The negative sign in electric field calculations represents the direction of the force exerted on a positive test charge. By convention, the direction of the electric field is taken to be the direction in which a positive test charge would move.
No, a negative electric field simply means that the direction of the electric field is opposite to the direction in which a positive test charge would move. A negative electric field still indicates the presence of an electric field.
Yes, an electric field can be both positive and negative depending on the location of the test charge. If the test charge is placed in a region where the electric field is directed towards the positive charge, the electric field will be positive. If the test charge is placed in a region where the electric field is directed towards the negative charge, the electric field will be negative.
Inside a conductor, the electric field is always zero because the free electrons in the conductor will rearrange themselves in such a way that the net electric field inside the conductor is canceled out. This is known as electrostatic equilibrium.
The electric field is inversely proportional to the square of the distance between two charges. This means that as the distance between two charges increases, the electric field decreases. Similarly, as the distance decreases, the electric field increases.