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 square's center 092 91 Number Units the tolerance is +/-2%

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)²cos45^o=(2kq1/a²)*cos45^o

E2x=2q2/a²)*cos45^o

E3x=(-2kq3/a²)cos45^o

E4x=(-2kq4/a²)cos45⁰

then in y direction

E1y=(-2kq1/a²)sin45^o

E2y=(2q2/a²)sin45

E3y=2kq3/a²)sin45

E4y=(-2kq4/a2)sin45

so adding all the electric field in x direction

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

so $\sum$Ex=0

now adding all electric field in y direction

$\sum$Ey=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