Two concentric conducing spheres of radii 4 cm and 12 cm are given equal but opposite charges of 6 x 10^-8C. How much energy is stored in the system?
How would I go about in beginning to solve this problem?
I think I would solve for E between the spheres using Gauss Law. Then, you have E as a function of r, and can integrate to find stored energy.
To solve this problem, you can use the formula for electric potential energy. The formula is given by:
U = k * (Q1 * Q2) / r
Where:
- U is the electric potential energy
- k is the Coulomb's constant (9 x 10^9 Nm^2/C^2)
- Q1 and Q2 are the charges on the spheres
- r is the separation between the spheres (which is the difference between their radii in this case)
In this problem:
- The charges on the spheres are given as equal but opposite, so Q1 = Q2 = 6 x 10^-8 C.
- The radii of the spheres are given as 4 cm and 12 cm, so the separation between them is r = (12 - 4) cm = 8 cm.
Now, you can substitute these values into the formula to calculate the electric potential energy (U).