What is Ex(P), the value of the x-component of the electric field produced by by the line of charge at point P which is located at (x, y) = (a,0), where a = 8.7 cm?

The value of the x-component of the electric field is -475213.968 newtons per coulomb.

In this question we shall apply Gauss' Law to determine the magnitude of the electric field (), in newtons per coulomb, rapidly and based on the assumptions of uniform charge distribution and cylindrical symmetry.

(1)

Where:

Based on all assumptions, we simplify (1) as follows:

And the equation of the x-component of the electric field is:

(2)

Where is the linear charge density, in coulomb per meter.

If we know that and , then the electric field produced by the line of charge at point P is:

The value of the x-component of the electric field is -475213.968 newtons per coulomb.

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The answer is below

Explanation:

We are going to use Gauss’ law to find the electric field equation. Since electric field is coming from an infinite line of charge, hence it is going out in a radial direction.  

Therefore we use the area of the electric field which passes through, forming a Gaussian cylinder. We neglect the ends of the area.

Hence:

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