Three identical particles, q 1, q 2, and q 3, each with charge q = 5.00 C , are
ID: 1523683 • Letter: T
Question
Three identical particles, q1, q2, and q3, each with charge q = 5.00 C , are placed along a circle of radius r = 2.00 m at angles 90, 180, and 270 degrees from the positive x axis, respectively. What is the resultant electric field at the center of the circle, point O? All angles are measured counterclockwise from the positive x axis.
SET UP
As always, consistent units are essential. With the value of k = 9.00×109 Nm2/C2 , distances must be in meters and charges must be in coulombs. If you are given centimeters or nanocoulombs, don't forget to convert.
Usually, you will use components to compute vector sums. Use proper vector notation; distinguish carefully among scalars, vectors, and components of vectors. Indicate your coordinate axes clearly on your diagram, and be certain that the components are consistent with your choice of axes.
SOLVE
In working out directions of E vectors, be careful to distinguish between the source point S and the field point P. The field produced by a positive point charge always points in the direction from source point to field point; the opposite is true for a negative point charge.
REFLECT
If your result is a symbolic expression, check to see whether it depends on the variables in the way you expect. If it is numeric, estimate what you expect the result to be and check for consistency with the result of your calculations.
Calculate the resultant electric field E at the origin, point O.
Enter the x component followed by the y component, separated by a comma, in newtons per coulomb.
Ex,Ey= N/CExplanation / Answer
net electric field = field due to each charge
electric field due to q1 (90 deg),
E1 = q / 4*pi*e0*r^2
E1 = 5*10^(-6) / 4*3.14*8.85*10^(-12)*2^2
E1 = 1.124*10^4 N/C (+y direction)
electric field due to q2 (180 deg),
E2 = q / 4*pi*e0*r^2
E2 = 1.124*10^4 N/C (-x direction)
electric field due to q3 (270 deg),
E3 = q / 4*pi*e0*r^2
E3 = 1.124*10^4 N/C (-y direction)
net electric field E = E1 + E2 + E3
E1 and E3 will cancle out each other
E = 1.124*10^4 N/C (-x direction)
Ex Ey = (1.124*10^4 i , 0) N/C
answer
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