Electric Field and Applications of Electrostatics
Senior 2 · Physics
Electric Field and Applications of Electrostatics
Lesson 4 of 5
18 min
Why does a lightning conductor end in sharp points, while the dome of a high-voltage generator is smooth and round? Why are you safer from lightning inside a car or a building than under a tree? The answers depend on how electric charge arranges itself on a conductor, and they save lives in Rwanda every rainy season.
In a conductor such as a metal, charges are free to move. Give a metal object some extra charge, and the like charges repel each other and spread out as far apart as they can. Within a tiny fraction of a second they come to rest (static equilibrium), and then:
A hollow metal can shows this clearly: touch the inside of a charged can with a small metal disc on an insulating handle (a proof plane) and carry it to a gold-leaf electroscope, and the leaf hardly moves. Touch the outside and the leaf rises. The charge is all on the outside.
Start with an example. Umutoni charges a pear-shaped metal conductor on an insulating stand. With the proof plane she samples three places and tests each sample on an electroscope:
The amount of charge on each square centimetre of surface, the surface charge density, is largest where the surface is most sharply curved.
| Shape | Charge distribution |
|---|---|
| Sphere | Uniform: the same charge density everywhere, because every part of the surface is curved equally |
| Pear-shaped | Greatest at the sharply curved narrow end, least on the flattest part |
| Pointed | Very high charge density at the point, so a very strong field just outside it |
Near a sharp point on a charged conductor, the field can become strong enough to pull electrons out of air molecules, turning the air into charged ions. Ions with the opposite sign to the point are attracted to it and cancel its charge; ions with the same sign are repelled, streaming away as an "electric wind" strong enough to bend a candle flame. The point therefore leaks charge into the air, a process called point discharge or corona discharge. In the dark it can glow faintly.
This has two consequences you will use in the next lesson:
Because the field inside a closed conductor is zero, a metal box or cage protects whatever is inside it from outside electric fields. This is called a Faraday cage. A car with a metal body is one: if lightning strikes it or a power line falls on it, the charge stays on the outside of the metal and the people inside are safe, as long as they do not touch the metal body. A building with a proper lightning-protection system protects its occupants in a similar way. A tree, a hut with a grass roof or an open field does not.
Tip
"Charge crowds at the points." Sharp curvature → high charge density → strong field → point discharge. Smooth and round → even charge → charge is kept.
In an explain-question about a hollow conductor, write both facts: "the excess charge resides on the outer surface" and "the field inside is zero".
Where does the excess charge on a charged hollow metal sphere reside, and what is the field inside it?
Solution: On the outer surface, spread uniformly. The field inside is zero.
Rank these parts of a charged pear-shaped conductor from highest to lowest charge density: flat side, pointed end, rounded broad end.
Solution: Pointed end > rounded broad end > flat side. Charge density is highest where the surface is most sharply curved.
A candle flame placed near a sharp point on a highly charged conductor bends away from the point. Explain.
Solution: The very strong field at the point ionises the air. Ions with the same sign as the point are repelled from it and stream away, dragging air with them. This "electric wind" blows the flame away from the point.
During a thunderstorm, Niyonzima's family is walking home. Should they shelter under a tall tree, or get into a nearby car with a metal roof? Explain.
Solution: The car. Its metal body acts as a Faraday cage: charge from a strike stays on the outside and the field inside is almost zero. A tall, isolated tree is a likely lightning target, and the current can jump from it to people sheltering underneath.
Remember
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