Peoples Physics Concepts

12.4. Electric Fields http://www.ck12.org

12.4 Electric Fields

• Describe what an electric field is and draw electric field lines.


• Calculate electric fields, find the direction a charge would move upon entering an electric field, and determine
  the force on that charge.

Students will learn what an electric field is, how to draw electric field lines and how to calculate electric fields.

They will also learn to apply the electric field in order to find the direction a charge would move upon entering the

field and the force on it.

Key Equations

E=kqr 2 ; Electric field due to chargeqat a distancerfrom the charge.

F=qE ; Force due to an electric field.

Guidance

Gravity and the Coulomb force have a nice property in common: they can be represented byfields. Fields are a kind
of bookkeeping tool used to keep track of forces. Take the electromagnetic force between two charges given above:

~Fe=kq^1 q^2

r^2

If we are interested in the acceleration of the first charge only — due to the force from the second charge — we can
rewrite this force as the product ofq 1 andkqr 22. The first part of this product only depends on properties of the object
we’re interested in (the first charge), and the second part can be thought of as a property of the point in space where
that object is.
In fact, the quantitykqr 22 captures everything about the electromagnetic force on any object possible at a distancer

fromq 2. If we had replacedq 1 with a different charge,q 3 , we would simply multiplyq 3 bykqr 22 to find the new force

on the new charge. Such a quantity,kqr 22 here, is referred to as the electric field from chargeq 2 at that point: in this

case, it is the electric field due to a single charge:

E~f=kq

r^2

The electric field is a vector quantity, and points in the direction that a force felt by a positive charge at that point

would. If we are given the electric field at some point, it is just a matter of multiplication — as illustrated above —

to find the force any chargeq 0 would feel at that point:

F~e

︸︷︷︸

Force on chargeq 0

= E~f

︸︷︷︸

Field

×q 0

︸︷︷︸

Charge

Force on chargeq 0 in an electric field

Note that this is true forallelectric fields, not just those from point charges. In general, theelectric fieldat a point

is the force apositive test charge of magnitude 1would feel at that point. Any other charge will feel a force along

the same line (but possibly in the other direction) in proportion to its magnitude. In other words, the electric field

can be thought of as "force per unit charge".

In the case given above, the field was due to a single charge. Such a field is shown in the figure below. Notice that

this a field due to a positive charge, since the field arrows are pointing outward. The field produced by a point