A rod and two balloons A very thin glass rod 4 meters long is rubbed all over wi

Question

A rod and two balloons A very thin glass rod 4 meters long is rubbed all over with a silk cloth. It gains a uniformly distributed charge 1.6 x 10^-6 C. Two small spherical rubber balloons of radius 1.2 cm are rubbed all over with wool. They each gain a uniformly distributed charge of -7 x 10^-8 C. The balloons are near the midpoint of the glass rod, with their centers 3 cm from the rod. The balloons are 2 cm apart (4.4 cm between centers). (a) Find the net electric field at the location marked by the x, 0.6 cm to the right of the center of the left balloon. Things to think about: Which objects make nonzero contributions to at this location? What are the correct distances from sources to the observation location? What is the direction of E due to the rod? (The drawing is not to scale; read the problem statement carefully. Assume the +/-x axis is to the right, the +/-y axis is up, and the +/-z axis is out.)

Explanation / Answer

Charge density on wire,d = Q/L
= (1.6*10^-6)/4
= 4*10^-7 C/m

Electric field due to wire = d (sin 45+cos 45)/2*pi*ebsoleneo*r
= 4*10^-7 *(1.4142) / (2*3.14*8.854*10^-12*0.03) (r is distance which is 3 cm = 0.03m)
= 3.4*10^5 N/C (-y)

Electric field due to left sphere = K*q/R1^2
= (9*10^9)*(-7*10^-8) / (0.006)^2   
= -1.75*10^7 N/C (x)

Electric field due to right sphere = K*q/R1^2
= (9*10^9)*(7*10^-8) / (0.032)^2   
= 6.15*10^5 N/C (x)

Net E = (6.15*10^5 -1.75*10^7 )x - 3.4*10^5 Y
= - 1.69*10^7 x - 3.4*10^5 Y

Y component can be ignored as it is very small than x compoenet.

So, E = 1.69*10^7 N/C in negative x direction

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