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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.

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Preciousorekha1

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

Ver imagen Preciousorekha1
lhmarianateixeira

In this exercise we have to use the knowledge of electric charges and calculate the magnitude and direction of this electric force, as

magnitude = 169.66N/C

direction = 8.6859°

Given from the question, we have that;

  • Length of line of charge L = 0.808 m
  • Linear charge density λ = 3.35 × 10⁻⁶ C/m
  • Q = -7.32 × 10⁻⁷ C
  • Coulombs force K= 8.99 × 10⁹ N·m²/C².

So with the information given earlier, we can use the Pythagorean theorem and calculate the magnitude like this:

[tex]tan \phi = 3.75 / (10.7 -1.56) = 22.3076\\E = 8.99 * 10^9 * 3.35 * 10^{-6} (0.808/ 10.7(10.7 - 0.808))\\E = 0.229905 *10^3 \\E = (8.99 * 10^9 * 7.32 * 10^{-7}) / ((3.75)^2 + (10.75-1.56)^2) = 0.6742 * 10^2\\E = - 0.62446 *10^2 + 0.2562 *10^2\\E = 169.66 N/C[/tex]

Now that we have the magnitude of the force we can calculate the direction of this force as:

[tex]Direction = tan \phi = 0.25621/1.6771 = 8.6859[/tex]

See more about eletric charges at brainly.com/question/14438235

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