To find the electric potential at point B, one must use the conservation of energy to relate the change in kinetic energy to the change in electric potential energy. The magnitude of the electric field is determined by the change in electric potential over the distance between two points. The direction of the electric field is from point A to point B.
To answer this question, we need to use the concept of electric potential energy and kinetic energy.
When a charge q moves in an electric field from point A to point B, its electric potential energy changes and can be converted into kinetic energy.
The electric potential V at any point is defined as the potential energy per unit charge, and the difference in electric potential energy between two points A and B is given by q(VA - VB).
The electric field E is defined as the force per unit charge exerted on a small positive test charge placed at a point in space.
A. To find the electric potential at point B, we use the conservation of energy.
The change in electric potential energy is equal to the negative of the change in kinetic energy: ΔPE = -ΔKE.
With q = -6.00×10-9 C and ΔKE = 5.00×10-7 J, the change in potential is ΔV = ΔPE / q. We already know VA = +30.0 V, therefore VB can be calculated.
B. The magnitude of the electric field E can be determined by the change in electric potential over a distance: E = ΔV / d, where d is the distance between points A and B.
C. The direction of the electric field is from a region of high electric potential to a region of low electric potential, which in this case is from point A to point B.
So, the correct answer is (b) from point A to point B.