The figure shows three point charges. Charge 1 and Charge 2 are on the x-axis, a

Question

The figure shows three point charges. Charge 1 and Charge 2 are on the x-axis, and Charge 3 is one the y axis. The value of the charges are Charge 1 equal to Q, charge 2 equal to 2Q, and Charge 3 equal to q. All the charges are equal distance, d, from the origin (x = y = 0). If Q = 2.0 nC, q = -0.4 nC, and d = 0.07 m, what is the magnitude of the total electric field at the origin, (x = y = 0)? Give your answer to three significant digits in units of N/C. Do not include the units in your answer.

Explanation / Answer

Distance of each of 3 charges from origin d = 0.07m

q1 = 2.0*10-9 C q2 = 4.0*10-9C q3 = -0.4*10-9C

Electric field due to q1 = E1= kq1 / d2
Direction depends on where the points are at
Electric field due to q1 =E1=9*109*2*10-9 / (0.07m)2
Electric field due to q1 =E1=3673.46 N/C
Direction:
q1 is at -0.07 m pointing towards the origin at 0 m. The direction from q1 to the origin is along the POSITIVE x-axis. Direction = +
E1 = ||E1|| * direction = 3673.46 N/C * (+) = 3673.46 N/C

Electric field due to q2 = E2= kq2 / d2
Electric field due to q2 = E2=9*109*4*10-9 / (0.07m)2
Electric field due to q2 = E2 =7346.93 N/C

Direction - the direction from q2 to the origin is in the NEGATIVE x direction, (-)
E2 = ||E2||*direction = 7346.93 N/C * (-) = -7346.93 N/C

Electric field due to q3 = E3= kq3 / d2
= E3=9*109*-0.4*10-9 / (0.07m)2

E3 = -734.69 N/C

Direction from q3 to the origin is also in the NEGATIVE y direction, ( - )

E3 = ||E3||*directoin = -734.69 N/C * (-) = 734.69 N/C

Net field = E = E1+ E2 + E3

E = 3673.46 N/C -7346.93 N/C +734.69 N/C

   E = - 2938.78

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