The potential of a coaxial cylinder with charge density 1 unit , inner radius 1m and outer cylinder 2m is (in 109 )

The potential difference (V) between two cylinders in a coaxial cable where the inner cylinder is charged, and the outer cylinder is grounded (or vice versa), can be found using Gauss’s Law for electric fields and the formula for the electric potential difference.

Given:

– Charge density (rho = 1) unit (assuming this is volumetric charge density (rho) in units of (text{C/m}^3), though typically, for coaxial cables, we use linear charge density (lambda) in units of (text{C/m})).

– Inner radius (a = 1) m

– Outer radius (b = 2) m

– The permittivity of free space (varepsilon_0 = 8.854 times 10^{-12} , text{F/m}) (Farads per meter)

For a coaxial cable, the electric field (E) at any point between the cylinders due to the inner charged cylinder can be found by applying Gauss’s Law:

[ E cdot 2pi r cdot L = frac{rho cdot (pi r^2 – pi a^2) cdot L}{varepsilon_0} ]

For (r > a), solving for (E),

[ E = frac{rho (r^2 – a^2)}{2 varepsilon_0 r} ]