Charged Metallic Balloon ( understanding a concept)

[Bailey]

the questioon is this:
A balloon of radius 34.5 cm is sprayed with a metallic coating so that the surface is conducting. A charge of 1.05 × 10-08 C is placed on the surface. What is the potential on the balloon's surface?

how i solved it:
-apply the Gauss law, which gives me the Electrical Field.

-apply the formula : Voltage = Ed ,

where E = electrical field , & d = distance traveled by charges (parrallel to field line)

n it turn out d = 34.5cm. this is where i don't get. why its d = 34.5cm?

its it b/c the positive charge move to the center, which travel a distance of 34.5cm? since if the surface is positively charged, it would repel the " + " charge to the centre & attact the " - " charge to surface...right?

 

[Doc Al]

how i solved it:
-apply the Gauss law, which gives me the Electrical Field.

No problem. You should get the field as a function of distance from the center, for points outside of the balloon: $E = kq/r^2$.

-apply the formula : Voltage = Ed ,

You must integrate from a reference point (usually infinity = 0 potential) to the balloon's surface.

where E = electrical field , & d = distance traveled by charges (parrallel to field line)

n it turn out d = 34.5cm. this is where i don't get. why its d = 34.5cm?

It's not. It turns out that the potential at a point a distance r from the center of the balloon (where r >= the balloon's radius) will equal kq/r.

 

[Andrew Mason]

n it turn out d = 34.5cm. this is where i don't get. why its d = 34.5cm?

its it b/c the positive charge move to the center, which travel a distance of 34.5cm? since if the surface is positively charged, it would repel the " + " charge to the centre & attact the " - " charge to surface...right?

Electrical potential is the work done to bring a unit +charge from infinity to the surface of the sphere, which is:

$$\int_{\infty}^{34.5} E\cdot ds = kQ(\frac{1}{R}-\frac{1}{\infty}) = \frac{1}{4\pi \epsilon_0}(\frac{Q}{34.5}-0)$$

AM

 

[Bailey]

ah, ic, thanks guy. it seem to clear thing up quite a bit.