Question

A finite line of charge with linear charge density λ = 3.35 × 10-6 C/m, and length L = 0.808 m is located along the x axis (from x = 0 to x = L). A point charge of q = -7.32 × 10-7 C is located at the point x0 = 1.56 m, y0 = 3.75 m. Find the electric field (magnitude and direction as measured from the x axis) at the point P which is located along the x axis at xP = 10.7 m. The Coulomb force constant k = 1/(4π ε0) = 8.99 × 109 N·m2/C2.

Answer 1

Answer: magnitude = 169.66N/C

direction = 8.6859°

Explanation:

Given from the question, we have that;

the Length of line of charge L = 0.808 m

Linear charge density λ = 3.35 × 10⁻⁶ C/m

charge q = -7.32 × 10⁻⁷ C

Coulombs force constant K = 1/(4π ε0) = 8.99 × 10⁹ N·m²/C².

NB. The picture uploaded gives a diagrammatic description of the problem.

From Pythagoras theorem we have,

tan Θ = 3.75 / (10.7-1.56)  

Θ = 22.3076 °

recall that the Electric field at point P due to the finite wire is;

È = Kλ (L / b(L+b)) Î .............. (1)

where È rep the electric field.

from equation 1, we have that  

È = 8.99 × 10⁹

where È rep the electric field.

from equation 1, we have that  

È = 8.99 × 10⁹ × 3.35 × 10⁻⁶ (0.808/ 10.7(10.7 – 0.808))

È = 0.229905 × 10³ N/C Î

recall also that the Electric field at point -P due to -q is;

È  = (8.99 × 10⁹ × 7.32 × 10⁻⁷) / ((3.75)² + (10.75-1.56)²) = 0.6742 × 10² N/C

where E = -E₁cosθÎ  + E₁sinθĴ

E = - 0.62446 ×10²Î   + 0.2562 ×10²Ĵ

The Resultant Electric charge Er is given as;

Er = 1.6771 ×10²Î + 0.2562 ×10²

Er =  [√(1.6771)² + (0.2562)² ] × 10² = 169.66 N/C

∴ Magnitude = 169.66 N/C

Having gotten the magnitude, let us find the direction;

⇒ Direction = tan Ф = 0.25621/1.6771 = 8.6859°

Direction = 8.6859°

cheers i hope this helps