Question

Calculate the electric field at distance of 320cm from an infinitely long wire carrying a charge per unit length equal to 8.3 C/m.

Answer 1

We can derive an expression for electric field using Gauss's Law.\[\int\limits_{}^{}EdA=\frac{ q _{enc} }{ \epsilon _{o} }\]For an infinite it is most appropriate to consider a Gaussian Surface that is cylindrical. Since the E-field is constant, the integral just becomes that of the differential of area, which would just be A. So, we get E times the area of a cylinder. This produces:\[E(2\pi rL)=\frac{ \lambda L }{ \epsilon _{o} }\]Therefore:\[E=\frac{ \lambda }{ 2\pi \epsilon _{o} r}=\frac{ 1 }{ 4\pi \epsilon _{o} }\frac{ 2\lambda }{ r } =2k \frac{ \lambda }{ r }\]Now, we have an equation that allows the information given to be applied. k is a constant, as you should know. Lambda is the charge per unit length, and r is the distance away from the charged line. Notice this equation makes sense, because Electric Field is a derivative of electrostatic force, so it is only dependent on 1/r instead of 1/r^2. Plugging in gives us:\[E=2(8.99x10^ { 9 })\frac{ 8.3 }{ 3.20 }=4.66 x 10^{10} N/C\]

Answer 2

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