Uniform Electric Fields
Electric Field Between Parallel Plates
A uniform electric field is one where the electric field strength is the same at every point. This occurs between two parallel plates with opposite charges.
NoteThe electric field lines between the plates are parallel and equally spaced, indicating a constant field strength.
Calculating Electric Field Strength
The electric field strength ($E$) between two parallel plates is determined by the potential difference ($V$) between the plates and the distance ($d$) separating them:
$$
E = \frac{V}{d}
$$
- Units: Electric field strength is measured in newtons per coulomb (N C$^{-1}$) or volts per meter(V m$^{-1}$).
- These units are equivalent.
- Consider two parallel plates separated by 0.05 m with a potential difference of 100 V.
- To find the electric field strength:
$$E = \frac{V}{d} = \frac{100 \, \text{V}}{0.05 \, \text{m}}$$
$$ = 2000 \, \text{V m}^{-1}$$
ExampleUniform electric fields are used in devices like capacitors and particle accelerators, where a consistent force on charged particles is needed.
Radial Fields
Fields Around Point Charges
- A radial electric field is created by a point charge or a spherical conductor.
- The field lines radiate outward from a positive charge and inward toward a negative charge.
The strength of a radial field decreases with distance, following an inverse square law.
Calculating Electric Field Strength in Radial Fields
The electric field strength ($E$) at a distance $r$ from a point charge $Q$ is given by:
$$
E = \frac{kQ}{r^2}
$$
where $k$ is the Coulomb constant ($8.99 \times 10^9 \, \text{N m}^2 \text{C}^{-2}$).
Calculate the electric field strength at a distance of 0.2 m from a positive charge of 5.0 μC.
Solution
$$E = \frac{kQ}{r^2}$$
$$ = \frac{8.99 \times 10^9 \times 5.0 \times 10^{-6}}{0.2^2}$$
$$ = 1.12 \times 10^6 \, \text{N C}^{-1}$$
Deflection of Charged Particles
How Charged Particles Move in Electric Fields
- Charged particles experience a force when placed in an electric field. This force causes them to accelerate.
- The force ($F$) on a charge ($q$) in an electric field ($E$) is given by:
$$
F = qE
$$
