Question

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?

Answer 1

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.