A -diameter parallel-plate capacitor with a spacing of is charged to . What are
(a) the total energy stored in the electric field and
(b) the energy density?
a. The total energy stored in the electric field is.
b. The energy density is
We have given that A -diameter parallel-plate capacitor with a spacing of is charged to
The total energy stored in a capacitor with capacitance when the potential difference is will be
As the capacitor is a parallel-plate type. So, we can substitute the capacitance as
From the first expression
Putting the values of the constants and variables
We need to find the energy density.
Let us consider the energy density denoted by , then
Using the numerical values in the equation. We get
An electric dipole at the origin consists of two charges q spaced apart along the y-axis.
a. Find an expression for the potential V(x, y) at an arbitrary point in the xy-plane. Your answer will be in terms of q, s, x, and y.
b. Use the binomial approximation to simplify your result from part a when s V x and s V y.
c. Assuming s V x and y, find expressions for Ex and Ey, the components of E u for a dipole.
d. What is the on-axis field E? Does your result agree with Equation 23.10?
e. What is the field E u on the bisecting axis? Does your result agree with Equation 23.11?
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