1. Concept Overview
An electric field is a way to describe how a charge influences the space around it. Instead of thinking about a force acting directly at a distance, the idea is that every charge creates a kind of invisible "field" around itself. Any other charge entering this space feels a force. This makes it easier to study how electric forces work in different situations.
2. Definition
Electric field at a point is defined as the force experienced per unit positive test charge placed at that point.
Mathematically:
\( \vec{E} = \dfrac{\vec{F}}{q} \)
Here, \( q \) is a small positive test charge used to measure the field.
3. Electric Field Due to a Point Charge
A point charge creates a symmetric electric field around it. The strength decreases as we move farther from the charge.
3.1. Formula
For a charge \( Q \), electric field at a distance \( r \) is:
\( E = k \dfrac{|Q|}{r^2} \)
The direction is:
- Radially outward if \( Q \) is positive
- Radially inward if \( Q \) is negative
3.2. Vector Form
\( \vec{E} = k \dfrac{Q}{r^2} \hat{r} \)
\( \hat{r} \) points away from the charge.
3.3. Physical Interpretation
Close to the charge, the field is strong. As distance increases, the field weakens quickly because of the \( 1/r^2 \) factor.
4. Electric Field Due to Multiple Charges
When more than one charge is present, each charge creates its own electric field. The total electric field is found by vector addition of all individual fields.
4.1. Superposition Principle for Fields
If charges produce fields \( \vec{E}_1, \vec{E}_2, \vec{E}_3, ... \) at a point, then:
\( \vec{E}_{\text{net}} = \vec{E}_1 + \vec{E}_2 + \vec{E}_3 + \cdots \)
This works because electric fields obey linearity.
5. Field Lines and Direction
Electric field is a vector, so it has a direction. We often draw field lines to visualise how the field behaves around a charge.
5.1. Rules for Direction
- A positive test charge moves along the direction of the electric field.
- Field lines start on positive charges and end on negative charges.
- Where lines are close together, the field is strong.
- Where they are far apart, the field is weak.
6. Worked Examples
6.1. Example 1: Field from a Single Charge
A charge \( Q = 5 \times 10^{-6} \text{ C} \) creates a field at a point \( 0.1 \text{ m} \) away. The electric field is:
\( E = k \dfrac{Q}{r^2} = 9 \times 10^9 \times \dfrac{5 \times 10^{-6}}{(0.1)^2} = 4.5 \times 10^6 \text{ N/C} \).
6.2. Example 2: Field from Two Charges
Two equal positive charges produce fields in opposite directions at the midpoint. Their magnitudes add or cancel depending on geometry. The net field is obtained using vector addition.
7. Physical Interpretation
You can imagine the electric field as the "influence" a charge creates in the surrounding space. A positive test charge placed in this region feels a push or pull depending on the direction and strength of the field. This viewpoint avoids the idea of direct action at a distance and makes it easier to analyse more complex charge distributions.