The figure below shows a hollow metal sphere with a positive point charge $Q$ sitting outside it. What is the electric field at the center of sphere ? The answer is zero (look at here at the beginning of page 4), but I do not understand why?
[Physics] Why is electric field zero inside a hollow metal sphere
chargeelectric-fieldselectrostaticshomework-and-exercises
Related Solutions
Your homework question is from http://panda.unm.edu/Courses/Malloy/PHYS161//Physics_161_Home_files/Lecture22.pdf
Which one is correct
b)
and why?
- Metal conducts.
- Charges can travel freely in a conductor.
- Like charges repel
- The charge carriers move as far apart as they can be
- The furthest apart they can be is evenly distributed over the outer surface.
See http://www.physlink.com/education/askexperts/ae28.cfm
I guess it is some kind of electrostatic induction - phenomena going on. Am I right?
I think not. See Wikipedia -"Electrostatic induction is a redistribution of electrical charge in an object, caused by the influence of nearby charges"
I understand that excess charge is distributed over hollow sphere
The whole charge, not just some excess (over what?), is distributed over the sphere.
negative and positive charges are distributed opposite sides
No, if there were both positive and negative charges on opposite sides they would not stay there, they would be attracted to one another and quickly cancel out.
but don't know which one positive or negative go to inside surface.
Neither.
What is capacitors?
See Wikipedia re capacitors.
When lightning strikes a car, it is not simply charge separation that protects the occupants; the conductive skin provides a preferential path for a current. If the charge were to simply be deposited on the skin of the car, something exciting might happen, but in fact the charge is carried through the car to the ground. It is definitely possible to apply a large enough current that ordinary conduction no longer occurs, but this isn't because the metal skin runs out of electron/hole pairs -- it's because the skin heats up and vaporizes!
Your premise for part 2 isn't quite correct. If you stick an electron inside a neutral, conductive sphere, you can still see the charge outside the sphere. If the sphere is grounded, then you will not, but that's because you've essentially hidden the charge on the ground and given the sphere an opposing charge.
Conductive shells shield their contents from external fields, but they do not shield the external environment from the charges of their contents.
If you add charge, grounding will continue to cancel your fields. If you increase the charge rapidly, then you can gain a momentary field, but currents will eventually cancel the charge accumulation. (Essentially, you are charging a capacitor, which is leaky because of connection to the ground.)
To return to the question you posed in part 1; what happens if we apply a slowly increasing field to a hollow conductive sphere that is perfectly insulated from ground? At first, polarization will shield the interior of the sphere from the external electric field. The conduction electrons will flow to create a polarization across the sphere. Eventually, however, the material will breakdown.
Exactly how is a matter of conjecture, on my part. Because the sphere will polarize, with electrons accumulating on one side and bare ion lattice on the other, I hypothesize that the ends of the sphere will begin to smear out perpendicular to the electric field. The electric field balances the repulsion between like species along the electric field, but not across it. Therefore, the ends of the sphere will experience a shear that thins them and breaks them. These broken pieces, being charged, then fly along the electric field at colossal speeds, allowing electric field into the erstwhile interior, and badly damaging your lab.
Best Answer
Suppose electric field inside the sphere is nonzero. Then since there is no charge inside the sphere and since electric lines of force do not form closed loops so we should be able to find two points A and B on the surface of sphere such that a line of force starts from A and ends at B, thus causing a potential difference between these points. But since the sphere is made of metal (which are usually good conductors) so there will be a flow of current between these two points until the potential difference between them vanishes. So in equilibrium i.e. when no current is flowing, electric field inside sphere should be zero.