Question

Chapter 22, Problem 007 n the figure the four particles form a square of edge length a-3.80 cm and have charges q1-7.74 nC, q2--18.9 nC, q3-18.9 nC, and q4--774 nC, what is the magnitude of the net electric field produced by icles at the squares center 092 91 Number Units the tolerance is +/-2%

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Answer #1

answer) we know the formula

E=kq/r2

first we have to find the electric field due to all the charges in x direction and then also in y direction

let a small positive charge in the middle as shown in the figure,

so first in x direction

E1x=kq1/r2

here r=a\sqrt{}2/ 2 ( from the figure)

so E1x=kq1/(a\sqrt{}2/2)2cos45o=(2kq1/a2)*cos45o

E2x=2q2/a2)*cos45o

E3x=(-2kq3/a2)cos45o

E4x=(-2kq4/a2)cos450

then in y direction

E1y=(-2kq1/a2)sin45o

E2y=(2q2/a2)sin45

E3y=2kq3/a2)sin45

E4y=(-2kq4/a2)sin45

so adding all the electric field in x direction

\sumEx=2kcos45/a2( q1+q2-q3-q4)=2kcos45/a2( 7.74nC-18.9nC+18.9nC-7.74nC)=0

so \sumEx=0

now adding all electric field in y direction

\sumEy=2ksin45/a2( -q1+q2+q3-q4)=2*8.99*109sin45/0.0382(-7.74*10-9-18.9*10-9+18.9*10-9-7.74*10-9)=1.36*105C

so the answer is 1.36*105 N/Cor 1.4*105 N/C

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