Electrostatics

The energy stored in a capacitor is given by the formula: U=‌

q2

2C

where U is energy, q is charge, and C is capacitance.
Step 2: Rearranging to Find Capacitance
We can solve for C as follows: C=‌

q2

2U

Here, q=12×10−6C and U=6J. Substitute these values into the formula:
C=‌

(12×10−6)2

2×6

Step 3: Calculate Capacitance
Simplify the above equation: C=12×10−12F
Step 4: Capacitance of a Spherical Conductor
The capacitance of a spherical conductor is given by: C=4πε0r
Step 5: Find the Radius
Rearrange to find the radius r:r=‌

C

4πε0

We can also use ‌

1

4πε0

=9×109Nm2∕C2 so:
r=9×109×12×10−12
Step 6: Solve for the Radius
Multiply the values: r=108×10−3=0.108m=10.8cm