184_notes:examples:week2_electric_field_negative

Example: Electric Field from a Negative Point Charge

Suppose we have a negative charge $-Q$ . What is the magnitude of the electric field at a point $P$ , which is a distance $R$ from the charge? Draw the electric field vector on a diagram to show the direction of the electric field at $P$ .

Facts

There is a negative charge $-Q$ .
The point $P$ is a distance $R$ away from the charge, with the orientation shown below in our representation.
The electric field from the point charge at a particular observation location can be written as $\vec{E} = \frac{1}{4\pi\epsilon_0}\frac{q}{r^2}\hat{r},$ where $q$ represents the charge, $r$ is the distance, and $\hat r$ is the unit-vector pointing from the point charge source to the observation location.

Representations

Negative Point Charge -Q, and Point P

Assumptions

Constant charge: Makes charge in electric field equation not dependent on time or space as no information is given in problem suggesting so.
Charge is not moving: This makes our separation vector fixed in time as a moving charge would have a changing separation vector with time.

Goal

Find the magnitude and direction of the electric field at $P$ .

Solution

Approximation

We approximate the charge with value $-Q$ as a point charge. This may not be the case, but our approximation does not seem unreasonable based on the limited information. In fact, this approximation is necessary, since we do not yet know how to represent electric field apart from the electric field from a point charge. We proce