Question

Three infinitely long wires having uniform linear charge density 2. are placed along x, y, and z-axis respectively.
Find electric field at point P(a, a, a).​

Answer 1

The net electric field at point p is E(net) = E 1 + E 2 + E 3 = λ / 4 π ε0 a (iˆ + jˆ + kˆ)

Explanation:

• Let us consider the electric field due to wire (3) only
• E 3=Euˆ  

E = λ / 2 π ε0 (a^2 + a^2 ) ^1 / 2  x (iˆ cos 45∘ + jˆ 45∘)

E = λ / 2 √2π ε0 a 1 / √2  (iˆ + jˆ)

E = λ / 4 π ε0 a (iˆ + jˆ)

Electric field due to wires (1) and (2)

E1  = λ / 4 π ε0 a (jˆ + kˆ)

E2 = λ / 4 π ε0 a (iˆ + kˆ)

E(net) = E 1 + E 2 + E 3 = λ / 4 π ε0 a (iˆ + jˆ + kˆ)