Question

Three point-like charges are placed at the corners of a square as shown in the figure, 24.0 cm on each side. Find the magnitude of the electric field at the center of the square. Let q11 = q33 = +28.0 µC and q22 = −24.0 µC.

Answer 1

E1 = k*q1/a^2

= 9*10^9*28*10^-6/0.24^2

= 4.37*10^6 N/c (towards +x axis)

E2 = k*q2/(2*a^2)

= 9*10^9*24*10^-6/(2*0.24^2)

= 1.87*10^6 N/c (45 degrees above -x axis)

E3 = k*q3/a^2

= 9*10^9*28*10^-6/0.24^2

= 4.37*10^5 N/c (towards -y axis)

so,

Enetx = E1 - E2*cos(45)

= 4.37*10^6 - 1.87*10^6*cos(45)

= 3.04*10^6 N/c

Enety = -E3 + E2*sin(45)

= -4.37*10^6 + 1.87*10^6*sin(45)

= -3.04*10^6 N/c

Enet = sqrt(Enetx^2 + Enety^2)

= sqrt(3.04^2 + 3.04^2)*10^6

= 4.29*10^6 N/c