6 Two uniformly charged nouconducting spheres of radius r 10

6. Two uniformly charged nou-conducting spheres of radius r- 10cm are placed on and on the the horizontal axis as shown in the figure. The surface charge density on the left sphere is right sphere is \'n-1.5× 10-4m7 I m above the origin. 3.5 × 10-3 .5x lhe vertical axis at . A negative point charge q-2pC is placed on the vertical sxis at t 20 1.09 -O s (m) 2 10 10 0 a. Calculate the magnitude and direction of the net electric field at the origin.

Solution

net charge on sphere on positive x axis=q2=1.5*10^-4*4(0.1)(0.1)=18.85 micro coulomb

net charge on sphere on negative x axis=q1=3.5*10^-4*4(0.1)(0.1)=43.98 micro coulomb

a) electric field at origin=Kq/r²

{K[18.85/2²]-K[43.98/2²]}i-{K[2/1²]}j

magnitude=6.4955

direction=tan^-1[{-K[2/1²]}/{K[18.85/2²]-K[43.98/2²]}]=197.658 clockwise from x-axis

b)net electric field at point charge q

x component={K[2*18.85/5^3/2]-K[2*43.98/5^3/2]}i=-40.46KN/C

y component={K[1*18.85/5^3/2]+K[1*43.98/5^3/2]}j=50.577KN/C

c)net force on point charge q={K[2*18.85/5^3/2](2i+j)+K[2*43.98/5^3/2]}(-2i+j)}=-40.46i+50.577j

d)net force on q =0

net horizontal force on point charge q={K[2*q2/5^3/2](2i)+K[2*43.98/5^3/2]}(-2i)}=0

q2=43.98*10^-6=1.5*10^-4*4r²

r=54.15cm