Section 2.2: Field of a Point Charge
This section derives the electric field due to a single point charge and explains the radial nature and magnitude using Coulomb's law.
Electric Field of a Point Charge:
\( \vec{E} = k \frac{q}{r^2} \hat{r} \)
Where \( k = 8.99\times10^9 \, \text{N·m²/C²} \), \( q \) is the point charge, \( r \) is the distance from the charge, and \( \hat{r} \) is the radial unit vector.
Example 1
A point charge \( q = 2 \mu C \) is located at the origin. Find the electric field at a point 0.5 m along the x-axis.
\( E = k \frac{q}{r^2} = 8.99\times10^9 \frac{2\times10^{-6}}{0.5^2} \approx 7.2\times10^4 \, \text{N/C} \)
Direction: along the +x-axis.
Practice Problems
- A point charge of \( -3\mu C \) is at the origin. Find the field 0.2 m away along the positive y-axis.
- Compute the field at a distance of 1 m from a charge of \( +5\mu C \).
- Compare the magnitudes of electric fields at 0.5 m and 1 m from the same point charge.
- Discuss the direction of \( \vec{E} \) for a negative point charge.
- Conceptual: Why does the field decrease with \( 1/r^2 \)?