# PHY C17: Electric Fields (A2)

Let’s dig deeper into electric fields now.

• Point Charges
• Coulomb’s Law
• Proportionality constant for Coulomb’s Law

Let’s go!

Just as we’ve discussed point masses under gravitation, it is useful to consider charged objects as being point charges.

What does being a point charge mean?
An object’s total charge is considered to be concentrated at 1 point.

When can we consider an object as a point charge?
Multiple objects can be seen as point charges if their size is much smaller than the distance between them.

There is another situation where the object can be considered as a point charge:
When charges are distributed equally on the surface of a sphere – which happens for conductors. Left: the actual objectRight: considering the object as a point charge

The electric field lines are perpendicular to the surface of the sphere, & act radially. Although the electric field actually radiates out from charges on the surface of the sphere, they appear to originate from the centre of the sphere.

In general, spherical conductors can be considered to be point charges at their centres for any point outside the sphere.

How about the electric field lines inside the sphere?
Inside a spherical conductor, the electric field is 0 (there is no electric force).

For a conductor at electrostatic equilibrium:

• Electric field inside a conductor is 0
• Why? If an electric field exists inside the conductor, mobile charges inside the conductor will move, & will eventually settle when there is no field inside
• Any net charges distribute themselves on the surface

What is the electric force?
As we’ve seen before, it is a force that acts on electrically-charged objects, & is repulsive between like charges & attractive between opposite charges.

Now we can look at it in detail.
Electric force follows an INVERSE SQUARE LAW:
“the strength of a field is inversely proportional to the square of the distance.”

Specifically, it follows Coulomb’s Law.

What is Coulomb’s Law?
“The force between 2 point charges is proportional to the product of both charges, & inversely proportional to the distance between the point charges.”

F ∝ q1q2/r2
F = kq1q2/r2

Which can also written as
F = kQq/r2

where k = 8.99 x 109 C-2Nm2

If you realise, this is similar to Newton’s Law of Gravitation, just with charge instead of mass!

There is a slight difference between the two – the proportionality constant: G for gravitation, k for electric force.

What is the proportionality for electric force?
k = 1/4πε0

It depends on this value ε0 called the permittivity of free space.

If that sounds scary, don’t worry – we will cover it in a later chapter (capacitance).
Basically, permittivity it is the ability of a medium to hold an electric field. Since we only deal with charges travelling around in a vacuum, we use the value of permittivity of a vacuum, or free space.

In our universe (not that we know of others), the value of ε0 is 8.85 x 10-12 C2N-1m-2

Plugging it into k = 1/4πε0 ,
k = 8.99 x 109 C-2Nm2

Don’t worry about permittivity just yet, you may use the value of k as 8.99 x 109 C-2Nm2 straightaway in calculations!