Question

A particle carrying a charge of 5.0 μC is located at the origin of a rectangular coordinate system, and a particle carrying a charge of 3.0 μC is located at (0, 5.0 m).

A.

What are the x and ycomponents of the magnitude of the electric field at the position (5.0 m, 0)?

Enter your answers numerically separated by a comma.

Ex, Ey =

B.

What are the x and ycomponents of the magnitude of the electric field at the position (-5.0 m, 0)?

Enter your answers numerically separated by a comma.

Ex, Ey= C. What are the x and ycomponents of the magnitude of the electric field at the position (0, -5.0 m)? Enter your answers numerically separated by a comma. Ex, Ey= Thank you

Answer 1

q1 = 5uC at x = 0,0
q2 = 3uC at x = 0,5

a)
Electric Field at x = 5,0
Ex due to Q1 = k*q1/r^2 = 8.9 * 10^3 * 5 / 25 = 1780 N
Ey due to Q1 = 0

Ex due to Q2 = k*q2/ (5^2 +5^2) cos(45) = 8.9 * 3 * 10^3 /35.35 = 755 N
Ey due to Q2 = k*q2/ (5^2 +5^2) sin(45) = 8.9 * 3 * 10^3 /35.35 =755 N

Ex = k*q1/r^2 + k*q2/ (5^2 +5^2) cos(45) = 1780 + 755 = 2535N
Ey =   k*q2/ (5^2 +5^2) sin(45) = 755 N

Ex = 2535N , Ey = 755N

b)
Electric Field at x = -5,0
Ex due to Q1 = k*q1/r^2 = 8.9 * 10^3 * 5 / 25 = 1780 N
Ey due to Q1 = 0

Ex due to Q2 = k*q2/ (5^2 +5^2) cos(45) =8.9 * 3 * 10^3 /35.35 = 755 N
Ey due to Q2 = k*q2/ (5^2 +5^2) sin(45) = 8.9 * 3 * 10^3 /35.35 = 755 N

Ex = k*q1/r^2 + k*q2/ (5^2 +5^2) cos(45) = 1780 + 755 = 2535N
Ey =   k*q2/ (5^2 +5^2) sin(45) = 755 N
Ex = 2535N , Ey = 755N

c)
Electric Field at x = 0,-5
Ex due to Q1 = 0
Ey due to Q1 = k*q1/r1^2

Ex due to Q2 = 0
Ey due to Q2 = k*q2/r2^2

Ex = 0
Ey = k*q1/r1^2 +  k*q2/r2^2
Ey = k *10^-6 (5/25 + 3/100)
Ey = 8.9 * 10^3 * 0.23
Ey = 2047 N

Ex = 0 , Ey = 2047 N