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An infinitely long straight wire has a uniform linear charge density of Derive the 4. equation for the electric field a distance R away from the wire using Gauss's Law for Electrostatics.

Respuesta :

Answer:

[tex]E = \frac{\lambda}{2\pi \epsilon_0 r}[/tex]

Explanation:

Let the linear charge density of the charged wire is given as

[tex]\frac{q}{L} = \lambda[/tex]

here we can use Gauss law to find the electric field at a distance r from wire

so here we will assume a Gaussian surface of cylinder shape around the wire

so we have

[tex]\int E. dA = \frac{q}{\epsilon_0}[/tex]

here we have

[tex]E \int dA = \frac{\lambda L}{\epsilon_0}[/tex]

[tex]E. 2\pi r L = \frac{\lambda L}{\epsilon_0}[/tex]

so we have

[tex]E = \frac{\lambda}{2\pi \epsilon_0 r}[/tex]

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