Consider a cylindrical capacitor composed of two concentric conducting cylinders with inner and outer radii, R_in and R_out. A strong, nonuniform electric field is created in the space between these cylinders, designed to ionize the air in this region. When the electric field strength exceeds the dielectric breakdown threshold of air (E_breakdown = 3.0 x 10⁶ N/C), air molecules in the region become ionized, resulting in free electrons and positively charged ions.
This ionization occurs in a specific cylindrical region around the inner conductor, extending to a radius r, which is typically five times the radius of the inner cylinder. In this setup, the inner radius of the cylinder is R_in = 0.15 mm, and the outer radius is R_out = 12.0 cm.
To generate the required electric field strength for ionization at a radius of r = 5.0 R_in, what potential difference V should be applied between the inner and outer conducting cylinders?

• A. 11 kV
• B. 15 kV
• C. 18 kV
• D. 27 kV