A positive charge of magnitude Q1 = 5.5 nC is located at the origin. A negative

Question

A positive charge of magnitude Q1 = 5.5 nC is located at the origin. A negative charge Q2 = -8.5 nC is located on the positive x-axis at x = 6.5 cm from the origin. The point P is located y = 5.5 cm above charge Q2.
Q1 = 5.5 nC
Q2 = -8.5 nC
x = 6.5 cm
y = 5.5 cm

Part (a) Calculate the x-component of the electric field at point P due to charge Q1. Write your answer in units of N/C.

  Part (b) Calculate the y-component of the electric field at point P due to charge Q1. Write your answer in units of N/C.
  Part (c) Calculate the y-component of the electric field at point P due to the Charge Q2. Write your answer in units of N/C.
  Part (d) Calculate the y-component of the electric field at point P due to both charges. Write your answer in units of N/C.
  Part (e) Calculate the magnitude of the electric field at point P due to both charges. Write your answer in units of N/C.
  Part (f) Calculate the angle in degrees of the electric field at point P relative to the positive x-axis.

Explanation / Answer

a) Ex1 = kQ1 / R^2 ( cos@)

Ex1 = k Q1 ( x / sqrt(x^2 + y^2) / (x^2 + y^2)

Ex1 = kQ1x / (x^2 + y^2)^1.5

Ex1= (9 x 10^9 x 5.5 x 10^-9 x 0.065 ) / (0.065^2 + 0.055^2)^1.5

Ex1 = 5212.09 N/C

b) Ey1 = kQ1 / R^2 ( sin@)

Ey1 = k Q1 ( y / sqrt(x^2 + y^2) / (x^2 + y^2)

Ey1 = kQ1y / (x^2 + y^2)^1.5

Ey1= (9 x 10^9 x 5.5 x 10^-9 x 0.055 ) / (0.065^2 + 0.055^2)^1.5

Ey1 = 4410.23 N/C

c) Ey2 = - kQ2 / y^2

Ey2 = - (9 x 10^9 x 8.5 x 10^-9) / (0.055^2) = - 25289.26 N/C

d) EY = Ey1 + Ey2 = - 20879.03 N/C

e) magnitude = sqrt(Ey^2 + Ex^2) = 21519.75 N/C

f) @ = tan^-1(20879.03/5212.09) = 75.98 deg belowe x axis

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