Electric field due to an infinitely long straight uniformly charged wire | Electromagnetics | Electrostatics

Electric field due to an infinitely long straight uniformly charged wire

The space around a charged particle in which another charge experience a force is known as electric field.
The electric field at any point due to infinitely long straight wire varies inversely with distance from the wire.

Electric field at P due to charge dq of length dy

$https://latex.codecogs.com/svg.image?dE=\frac{kdq}{(MP)^{2}}=\frac{kdq}{x^{2}}$

The charge on length dy, dq = λ dy

$https://latex.codecogs.com/svg.image?dE=\frac{k\lambda dy}{x^{2}}$

This electric field will be along MP

Total electric field at P

$https://latex.codecogs.com/svg.image?E=\int dE_{x}+\int dE_{y}$

Due to symmetry

$https://latex.codecogs.com/svg.image?\int dE_{y}=0$

$https://latex.codecogs.com/svg.image? \because dE_{x}=dE cos\theta$

Therefore

$https://latex.codecogs.com/svg.image?\therefore E = \frac{2k\lambda }{r}$

This electric field will be along PX

To know more about this lecture please visit on https://youtu.be/3Tw02vIpD2s

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