Section 4.1: Electric Field Concepts
An electric field is a region of space around a charged object where other charges experience a force. Understanding electric field lines and their properties is essential for analyzing charge interactions.
Key Concepts:
- Electric Field Definition: \( \mathbf{E} = \frac{\mathbf{F}}{q} \)
- Unit: Newton per Coulomb (N/C)
- Direction: Away from positive charges, towards negative charges
- Point Charge Field: \( E = k \frac{Q}{r^2} \)
Example 1
A 2 μC charge experiences a force of 0.06 N. Find the electric field at its location.
\( E = F/q = 0.06 / 2 \times 10^{-6} = 3 \times 10^4 \text{ N/C} \)
Example 2
A point charge Q = 5 μC is placed at a distance of 0.2 m. Find the magnitude of the electric field.
\( E = k Q / r^2 = (9 \times 10^9)(5 \times 10^{-6}) / 0.2^2 = 1.125 \times 10^6 \text{ N/C} \)
Practice Problems
- Find the electric field at a point 0.5 m from a charge of 10 μC.
- A 3 μC charge experiences an electric force of 0.09 N. Determine the field strength.
- Calculate the field due to two point charges, 4 μC and -2 μC, 1 m apart at a midpoint.
- Sketch electric field lines for a positive and a negative point charge.
- A 5 μC charge is placed 0.1 m from another 2 μC charge. Compute the force and field.
- Determine the net electric field at the center of a square with charges at each corner.
- A 1 μC charge is placed near a -2 μC charge. Find the acceleration if the mass is 0.01 kg.
- Compute the electric field at 0.2 m from a 8 μC point charge.
- Explain the direction of the field between two opposite charges.
- Two charges, +3 μC and +5 μC, separated by 0.4 m. Find the net field at the midpoint.