(6%) Problem 16: Consider the point charges arranged at the corners and at the c

Question

(6%) Problem 16: Consider the point charges arranged at the corners and at the center of a square, as depicted in the figure da Go gc Id Otheexpertta.com × Find the magnitude of the electric field, in newtons per coulomb, at the location of qa in the figure, given that qb = qc-9a-3.1 nC , q = -0.2 nC, and the square is 6 cm on a side Grade Summary Potential Submissions 0% 100% sin cotan0 asinO acosO atan) acotan)sinh(0 cosh0nh cotanh0 tan() | | ( 78 9 Attempts remaining: 18 % per attempt) detailed view 0% 0% 0 END Degrees O Radians DELCLEAR Submit I give up! Hints: 3 for a 0% deduction. Hints remaining: 0 Feedback: 0%-deduction per feedback. How does the electric field combine from different sources? The principle of superposition allows us to just add the electric field vector from any number of sources. Draw a picture of the electric field at qa, and try to make it to scale. This will help you see what the answer should be Just remember that you have to add the vector quantity, not just the magnitude from each point.

Explanation / Answer

at the location of a,

|Ec| = |Eb| = k*qc/d^2

= 9*10^9*3.1*10^-9/0.06^2

= 7750 N/c

|Ed| = 9*10^9*3.1*10^-9/(2*0.06^2)

= 3875 N/c

|E| = k*q/(sqrt(2)*d/2)^2

= 9*10^9*0.2*10^-9/(sqrt(2)*0.06/2)^2

= 1000 N/c

Enetx = Ebx + Ecx + Edx + Ex

= -7750 + 0 - 3875*cos(45) + 1000*cos(45)

= -9782 N/c

Enety = Eby + Ecy + Edy + Ey

= 0 + 7750 + 3875*sin(45) - 1000*sin(45)

= 9782 N/c

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

= sqrt(9782^2 + 9782^2)

= 13834 N/c

= 1.4*10^4 N/c (when rounding to two significant figures)

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