Electrostatics -Electric Field and Potential

[abelthayil]

Homework Statement

A 30 cm diameter metal sphere hangs from a thread in the middle of a very large room. So its surroundings are essentially at infinity. If the electric field at tis surface is equal to the break down strength of air 3MV/m, what is the absolute potential at the center of the sphere?
A) 450 kV
B) 150 kV
C) 300 kV
D) 0

The answer is from what I've searched online is A


2. The attempt at a solution


The Electric FIeld at the surface is 3,000,000 V/m so kQ/r²=3,000,000
The only unknown is charge and solving we get Q=3*10⁶*r²/k
where (k=1/4pi epsilon nought)

so potential at the centre =kQ/r=9* 10⁵ V which is wrong so help please..

 

[ehild]

Your method is correct, V=kQ/r, so E=kQ/r^2, V=Er...but you have to use r=0.15 m, instead of 0.3m. It is the radius.

ehild

 

[abelthayil]

Oh YES ! How silly of me Thanks !