What potential difference vwc between the wire and the cylinder produces an electric field of 2.00*104 volts per meter at a distance of 1.20 centimeters from the axis of the wire? (assume that the wire and cylinder are both very long in comparison to their radii?

The expression for potential difference:

V (wc) = Er · (ln (rc / rw) · r)

where: Er = 2 · 10^4 V/m = 20,000 V/m,

rc = 1.8 cm = 0.018 m

rw = 145 micrometers = 0.000145 m,

r = 1.2 cm = 0.012 m (a distance from the axis of wire).

V (wc) = 20,000 V/m · (ln (0.018 / 0.000145) · 0.012 m) =

= 20,000 V/m · (4.82 · 0.012 m) =

= 20,000 V/m · 0.05784 = 1,157 V

Answer: The potential difference is 1,157 V.