An infinitely long line charge of linear charge density λ lies parallel to the y-axis along x = 0, z = 2 m. The electric field at point P(1,1,1) m is:
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An infinitely long line charge of linear charge density λ lies parallel to the y-axis along x = 0, z = 2 m. The electric field at point P(1,1,1) m is:

G1 Physics · Accepted Answer

The perpendicular vector from the line to P is r⃗_⊥ = î - k̂. Thus, r ⊥ r_⊥ r ⊥ ​ = √2, r̂_⊥ = (î - k̂)/√2. For an infinite line charge, E = λ/(2πε₀ r ⊥ ) . r_⊥). r ⊥ ​ ) . Hence, E⃗ = [λ/(2πε₀√2)]·[(î-k̂)/√2] = [λ/(4πε₀)](î-k̂).