4. A very long conducting cylinder of a radius of 2 cm has a uniform linear char

Question

4. A very long conducting cylinder of a radius of 2 cm has a uniform linear charge density a) What is the potential (in Volts) at the cylinder's surface with respect to infinitely distant point in space? b) What is the difference in potential, Vz-V1, between two points located at distances of 3 cm (point 1) and 8 cm (point 2) away from the surface. c) How much farther or closer point 2 needs to be shifted in space from its original location for the potential difference to double in magnitude? d) Bonus question (carries 25 extra points for the problem): What is the potential at a point that is 1 cm away from the cylinder's axis?

Explanation / Answer

a] V = 2k lambda ln (b/a)

= infinity.

b] delta V = 2k lambda* ln (b/a) = 2*9e9*5e-3* ln (8/3) = 8.83*10^7 V

c] To double potential difference, deltaV = 2*2*9e9*5e-3* ln (8/3)

=2*9e9*5e-3* ln (8/3)^2 = 2*9e9*5e-3* ln (64/9) = 2*9e9*5e-3* ln (21.3/3)

Point 2 needs to be shifted at 21.3 cm means 13.3 cm further

d] Potential will be equivalent to that on surface as electric field inside conductor is zero. So potential is infinity.

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