First slide

Finding field strength using Gauss's Law

Question

A infinitely long non-conducting cylinder of inner radius 5 cm and outer radius 7 cm has uniform volume charge density $ρ = 8.85 x 10^{- 9} C / m^{3}$ . The magnitude of electric field at a distance of 10 cm from axis of the cylinder is

Moderate

A

12 N/C
B

6 N/C
C

18 N/C
D

24 N/C

Solution

$E = \frac{2 kλ}{r} = \frac{2 k}{r} [π ({r_{2}}^{2} - {r_{1}}^{2}) ρ] E = \frac{2 x 9 x 10^{9}}{10^{- 1}} [π (49 - 25)] x 10^{- 4} x 8.35 x 10^{- 9} = 12 N / C$

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