What are the strength and direction of the electric field at the position indica

Question

What are the strength and direction of the electric field at the position indicated by the dot in the figure(Figure 1)?https://session.masteringphysics.com/problemAsset/1384377/2/27.P28.jpg Part A: Give your answer in component form. (Assume that x-axis is horisontal and points to the right, and y-axis points upward.) Express your answer in terms of the unit vectors i^ and j^. Express your answer using two significant figures. PartB: Give your answer as a magnitude and angle measured cw from the positive x-axis. Express your answer using two significant figures. Part C: CW from the +x-axis Express your answer using two significant figures.

Explanation / Answer

Electric Field due to point charge is given by, E = k*q/r^2

Due to 5.0 nC Charge,

E1 = (9.0*10^9*5.0*10^-9)/(2*10^-2)^2 i^
E1 = 112500 N/C i^

Due to - 5.0 nC Charge,
E2 = (9.0*10^9*5.0*10^-9)/(4*10^-2)^2 j^
E2 = 28125 N/C j^

Due to 10.0 nC Charge,
Distance btw the Charge and point, = sqrt(2^2 + 4^2) = 4.47 cm

E3 = (9.0*10^9*10.0*10^-9)/(4.47*10^-2)^2 * 2/4.47 i^ - (9.0*10^9*10.0*10^-9)/(4.47*10^-2)^2 * 4/4.47 j^
E3 = 20153.5 i^ - 40306.9 j^ N/C

Enet = E1 + E2 + E3
Enet = 112500 i^ + 28125 j^ + 20153.5 i^ - 40306.9 j^
Enet = 132654 i^ - 12181.9 j^
In two sig Fig,
Enet = 1.3 * 10^5 i^ - 1.2 * 10^4 j^ N/C

(B)

|Enet | =133212 N/C
In two sig fig,
|Enet| = 1.3 * 10^5 N/C

(C)
Angle = tan^-1( 1.2 * 10^4) / (1.3 * 10^5)
Angle = 5.274o Clock wise from +vex axis.

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