A spherical metal dome of radius 15cm is electrically charged. it has a positive charge of 2.5μC distributed uniformly on its surface. Calculate the electric field strength at the surface of the dome.

Question

stormfire1 · Answer

$$E=\frac{Q}{4pi \epsilon_0r^2}$$
You know Q and r so you have all the values you need to solve for the field.

stormfire1 · Answer

This may help if you're unclear: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesph.html#c3

anonymous · Answer

E = 2.5
4π8.85*10^ˉ¹² *(0.15)² =2.9*10^10

anonymous · Answer

Is the calculation correct?

stormfire1 · Answer

Gotta find my calculator...just a minute :)

stormfire1 · Answer

$$\frac{2.5 x 10^{-6}C}{4pi*8.85x10^{-12}*(0.15m)^2}=9.99 x 10^5 N/C$$

anonymous · Answer

I dont get the same answer i dont know why?

stormfire1 · Answer

Are you typing it in as I did above into your calculator or doing it some other way?

anonymous · Answer

I,m typing in the same way into the calculator!

stormfire1 · Answer

ok, let me make sure *I* typed into my calculator right...

anonymous · Answer

Ok

stormfire1 · Answer

Sorry...phone.  I still get the same answer

stormfire1 · Answer

2.5E-6/(4*pi*8.85E-12*(0.15)^2) = 999089.4105

stormfire1 · Answer

That's exactly how I typed it in

anonymous · Answer

Ok i will try it again!

anonymous · Answer

Yes i get 999089.4105

stormfire1 · Answer

good :)  I thought I was going crazy.

anonymous · Answer

Okay i have a follow on question. Explain how the answer would change at a distance of 30cm from the surface of the dome?

stormfire1 · Answer

Well, if you double the radius in the formula you will get 4 times less field (because the radius is squared in the denominator).  You can plug it into the formula to see that.

anonymous · Answer

I got 249772.3526?

stormfire1 · Answer

Yep... 1/4th of what it was at 15cm

anonymous · Answer

Ok good. So is the answer 2.5*10^5?

stormfire1 · Answer

Yes

stormfire1 · Answer

I think the question doesn't really want the numerical answer though.  I believe it wants you to explain that it will be 4 times less that it was at 15cm because the radius is squared in the denominator.

stormfire1 · Answer

This is a common type of physics question...it wants you to understand how changing the radius (doubling it, halfing it, etc) affects the answer.

anonymous · Answer

ok thanks