# physics

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10. A length L of wire has a charge density of  C/m. What is the electric field at an axial distance r from the wire if L is 5 meters,  is 5 x 10-8 C/m and r is 10 cm. Use Gauss’s Law to solve.

• not a radial distance r? -

I suspect a typo here.
Yes, use Gauss's law if the length is great compared to the distance r
here L = 5 and r = 0.1
Area of cylinder around wire at distance r is 2 pi r L

integral of E coming out of surface = charge inside /eo
so
2 pi r L E = 5*10^-8 L /eo
so
E = 5*10^-8 /(2 pi eo) = 10*10^-8 /(4 pi eo)

= 10^-7 k

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