Question

An infinite line charge of linear density λ = 0.30 μC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m. The x component of the electric field at the point P on the x axis at x = 3.0 m is approximately . A) 1.8 kN/C B) 4.2 kN/C C) 0.96 kN/C D) 5.2 kN/c E) 0.64 mN/C

Answer 1

The line charge E-field Ec = λ/(2πr*e0),
where λ = charge/length and e0 is the permittivity constant = 8.8542E-12 F/m.
The point charge E-field Ep = kq/r^2 where electrostatic constant k = 1/(4π*e0) = 8.99E9 N-m^2/C^2.

Answer 2

D) 5.2 kN/c

Step-by-step explanation:

Electric field due to infinity line charge

λ /2πε₀r = .3 x 10⁻⁶ x 2 x 9 x 10⁹ / 3 = 1.8 x 10³. It will be towards x axis.

Electric field due to point charge = k.q / r² = 9 x 10⁹ x 6 x 10⁻⁶ / 13 = 4.15 x 10³

x component of this field = 4.15 x 10³ x cos Ф = 4.15 x 10³ x 3 / √13

3.458 x 10³

Total electric field = 5.2 kN / C.