A semi-infinite straight line charge of uniform linear charge density λ occupies the negative x-axis, from x = -∞ to x = 0. A point P is at (0,a), where a>0. The magnitude of the electric field at P is:
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Question

A semi-infinite straight line charge of uniform linear charge density λ occupies the negative x-axis, from x = -∞ to x = 0. A point P is at (0,a), where a>0. The magnitude of the electric field at P is:

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G1 Physics · Accepted Answer

Take a source element at (-s,0), with s≥0. dE⃗ = kλ ds (s î + a ĵ)/(s²+a²)³ᐟ². Thus, Eₓ = kλ ∫₀^∞ s ds/(s²+a²)³ᐟ² = kλ/a, Eᵧ = kλa ∫₀^∞ ds/(s²+a²)³ᐟ² = kλ/a. Hence, E = √(Eₓ²+Eᵧ²) = √2 kλ/a.

A semi-infinite straight line charge of uniform linear charge density λ occupies the negative x-axis, from x = -∞ to x = 0. A point P is at (0,a), where a&gt;0. The magnitude of the electric field at P is:

A semi-infinite straight line charge of uniform linear charge density λ occupies the negative x-axis, from x = -∞ to x = 0. A point P is at (0,a), where a>0. The magnitude of the electric field at P is: