Section 3.2: Electric Fields
The electric field is a region of space around a charged particle in which another charged particle experiences a force. It is defined as the force per unit charge:
\[ \vec{E} = \frac{\vec{F}}{q} \]
- \(\vec{E}\) = electric field (N/C)
- \(\vec{F}\) = force experienced by a test charge (N)
- \(q\) = magnitude of the test charge (C)
For a point charge \(Q\), the electric field at a distance \(r\) is:
\[ \vec{E} = k \frac{Q}{r^2} \hat{r} \]
Example: Electric Field of a Point Charge
Calculate the electric field at a point 0.3 m from a charge \(Q = 4 \, \mu\text{C}\).
\[ E = \frac{(8.99 \times 10^9)(4 \times 10^{-6})}{(0.3)^2} \approx 3.996 \times 10^5 \, \text{N/C} \]
Practice Problems
- A point charge of -2 μC creates an electric field at a point 0.25 m away. Calculate its magnitude and direction.
- Two charges +3 μC and -3 μC are placed 0.4 m apart. Find the electric field at the midpoint between them.
- Explain why the electric field is a vector quantity and how vector addition is used for multiple charges.
- Derive the relationship between electric field and electric potential for a point charge.
- A small test charge of +1 μC experiences a force of 0.02 N. Determine the electric field at its location.