Capacitors

Energy Stored in a Charged Capacitor
The energy stored in a charged capacitor is given by the formula:
where: - is the capacitance of the capacitor,
- is the voltage across the capacitor.
Capacitance of a Spherical Capacitor:
For a spherical capacitor (or a sphere with charge), the capacitance is given by:
where: - is the permittivity of free space,
- is the radius of the sphere.
Given , we can calculate the capacitance:

Voltage across the Spherical Capacitor:
The voltage across the capacitor is related to the charge and capacitance by the formula:
Given the charge , we can calculate the voltage:

Energy Stored in the Capacitor:
Now, we can calculate the energy stored in the capacitor using the formula :
Thus, the energy stored in the charged capacitor is 1.20 joules.
Electric Field at a Distance of 20 cm from the Center of the Sphere:
The electric field at a distance from the center of a spherical charge distribution is given by:
where:
- is the charge on the sphere,
- is the distance from the center of the sphere (20 cm).
Substituting the values:
Thus, the electric field at a distance of 20 cm from the center of the sphere is .