Question

To understand the relationship and differences between electric potential and electric potential energy. In this problem we will learn about the relationships between electric force F⃗ , electric field E⃗ , potential energy U, and electric potential V. To understand these concepts, we will first study a system with which you are already familiar: the uniform gravitational field. F⃗ (z) =−mgk^ 1)Now find the gravitational potential energy U(z) of the object when it is at an arbitrary height z. Take zero potential to be at position z=0. Keep in mind that the potential energy is a scalar, not a vector.

2)Express U(z) in terms of m, z, and g. Find the electric potential V of the uniform electric field E⃗ =Ek^. Note that this field is not pointing in the same direction as the field in the previous section of this problem. Take zero potential to be at position z=0. Express V in terms of q, E, and z.

3)The electric field can be derived from the electric potential, just as the electrostatic force can be determined from the electric potential energy. The relationship between electric field and electric potential is E⃗ =−∇⃗ V, where ∇ is the gradient operator: Find an expression for the electric field E⃗ in terms of the derivative of V. Express your answer as a vector in terms of the unit vectors i^, j^, and/or k^. Use dV/dz for the derivative of V with respect to z.

Answer 1