**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.

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 ∝ q_{1}q_{2}/r^{2}**F = kq _{1}q_{2}/r^{2}**

Which can also written as**F = kQq/r ^{2}**

where **k = 8.99 x 10 ^{9} C^{-2}Nm^{2}**

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 = 1/4πε _{0}**

It depends on this value ε_{0} 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 ε_{0} is 8.85 x 10^{-12} C^{2}N^{-1}m^{-2}

Plugging it into k = 1/4πε_{0} ,**k = 8.99 x 10 ^{9} C^{-2}Nm^{2}**

Don’t worry about permittivity just yet, you may use the value of k as 8.99 x 10^{9} C^{-2}Nm^{2} straightaway in calculations!

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