Physics question about electrical charges?

Question

In the figure, four charges, given in multiples of 1.00×10-5 C form the corners of a square and four more charges lie at the midpoints of the sides of the square. The distance between adjacent charges on the perimeter of the square is d = 3.60×10-2 m. What are the magnitude and direction of the electric field at the center of the square? The magnitude of E?

here is the figure http://img404.imageshack.us/my.php?image=myimagecw0.jpg

~<3 jessica

Answer 1

The electric field vectors due to:

the conner &quot;+3q&#039;s&quot; cancel

the north/south &quot;+q&#039;s&quot; cancel

q=1.0*10^-5 C

d=3.6*10^-2 m

E=K*q/r^2

**************************************...

The electric field vectors due to

the conner charges +5q and |-5q| add at center

r^2=d^2+d^2

r^2=2*(3.6*10^-2)^2

= 0.002592

E=2*(9*10^9*5*q/r^2)

= 2*(9*10^9)*5*(1.0*10^-5)/(0.002592)

= 347,222,222 N/C @ 45 &quot;northeast&quot;

**************************************...

The electric field vectors due to

the +q  and |-2q|  charges add at center&quot;

d=3.6*10^-2 m

Ew=9*10^9*1*q/d^2

(9*10^9)*1*(1.0*10^-5)/(3.6*10^-2)^2

= 69,444,444 N/C East------&gt;

Ee=9*10^9*2*q/d^2 @ 0

9*10^9*2*(1.0*10^-5)/(3.6*10^-2)^2

= 138,888,888 N/C      East-------&gt;

ET=69444444+138888888 = 208333332 @ 0 degrees East-------&gt;

**************************************...

sum x components:

347222222*Cos(45)+ 208333332*Cos(0) =453,856,519 i

sum y components:

347222222*Sin(45)+ 208333332*Sin(0)=245,523,187 j

&quot;at center&quot;

Resultant E =  516,011,023 N/C

Angle with the positive x-axis: =28.41 degrees