ANSWERS MUST BE CORRECT: (Detailed explanation of order of processes required. T

Question

ANSWERS MUST BE CORRECT: (Detailed explanation of order of processes required. Take your time and answer it perfectly to receive credit. The most detailed answer and explanation will be awarded points).

Three charges are located at (respectively):

+3.2?C        (-0.20m , 0.17m )

-5.1?C         (0.51m , -0.30m )

-6.7?C         (-0.48m , -0.39m )

QUESTION:        

What is the electric field at the origin?     (Enter the x and y components of the field separated by a comma).

                            Ex,Ey = Ex? , Ey?       N/C

Explanation / Answer

Distance of 3.2C from origin=r1= sq rt[(-0.2)^2 + (0.17)^2] = 0.262 m and angle with X-axis is 40.45 degree

Distance of -5.1C from origin=r2= sq rt[(0.51)^2 + (-0.3)^2]= 0.5916 m and angle with X-axis is 30.47 degree

Distance of -6.7C from origin=r3= sq rt[(-0.48)^2 + (-0.39)^2]= 0.618 m and angle with X-axis is 39.128 degree

Electric field due to 3.2C = E1 = 3.2 / [ 4*pi*epsilon*r1^2] = 419.089 * 10^9 N/C

Electric field due to -5.1C = E2 = (-5.1 )/ [ 4*pi*epsilon*r2^2] = -131 * 10^9 N/C

Electric field due to -6.1C = E3 = -6.1 / [ 4*pi*epsilon*r3^2] = -157.7 * 10^9 N/C

electric field direction:

3.2 C : from origin to charge

-5.1C : from charge to origin

-6.1C : from charge to origin

now ,resultant electric field"

Ex = -E1*cos40.45 - E2*cos30.47 + E3*cos39.128 = -328.27 * 10^9 N/c

Ey = E1*sin40.45 + E2*sin30.47 + E3*sin39.128 = 105.89 * 10^9 N/c

so E = Ex + Ey = 1.089* 10^7 N/c

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