Electric Circuits and Capacitance: Calculating Voltages in Coaxial Cylinders

The challenge in determining voltages between coaxial conducting cylinders lies in calculating the capacitance of the system based on the given radii and length, and then using it to calculate the voltages between the middle cylinder and the other two. Can you calculate the voltages in this scenario?

To find the voltages between the middle cylinder and the other two coaxial cylinders, we first need to calculate the capacitance of the system. The capacitance of a coaxial capacitor is given by the formula:

C = (2πε₀L)/ln(b/a)

Substitute the given values for the radii and length into the formula to find the capacitance:

C = (2πε₀10)/(ln(1/0.5) + ln(2/0.5))

Once we have calculated the capacitance, we can use the formula:

V = Q/C

Substitute the given charge and capacitance values into the formula to calculate the voltages between the middle cylinder and the other two coaxial cylinders. This will give you the voltages V₁ and V₂ for the system.