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 , electric field , potential energy , and electric potential . To understand these concepts, we will first study a system with which you are already familiar: the uniform gravitational field.
Now find the gravitational potential energy of the object when it is at an arbitrary height . Take zero potential to be at position .
(Express in terms of , , and . Note that because potential energy is a scalar, and not a vector, there will be no unit vector in the answer).
Now find the potential energy of this charged particle when it is at height . Take zero potential to be at position .
(Express (a scalar quantity) in terms of , , and .)
The SI unit for electric potential is the volt. The volt is a derived unit, which means that it can be written in terms of other SI units. What are the dimensions of the volt in terms of the fundamental SI units?
(Express your answer in terms of the standard abbreviations for the fundamental SI units: (meters), (kilograms), (seconds), and (coulombs))
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 , where is the gradient operator:
.The partial derivative means the derivative of with respect to , holding all other variables constant.
Consider again the electric potential corresponding to the field . This potential depends on the z coordinate only, so and .
Find an expression for the electric field in terms of the derivative of .
Express your answer as a vector in terms of the unit vectors , , and/or . Use for the derivative of with respect to .