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.
The 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:
$$E = \frac{V}{d} = \frac{100 \, \text{V}}{0.05 \, \text{m}}$$
$$ = 2000 \, \text{V m}^{-1}$$
Uniform 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:
$$
F = qE
$$
Charge in a uniform electric field
A proton in a uniform electric field of 5000 V m$^{-1}$ experiences a force of:
$$F = qE$$
$$ = (1.6 \times 10^{-19} \, \text{C})(5000 \, \text{V m}^{-1})$$
$$ = 8.0 \times 10^{-16} \, \text{N}$$
Applications in Cathode Ray Tubes
Cathode ray tubes (CRTs) use electric fields to deflect electrons and create images on a screen.
- Electrons are accelerated by a uniform electric field between parallel plates.
- The deflection of electrons is controlled by adjusting the electric field strength.
The direction of deflection depends on the charge of the particle:
- Positive charges move in the direction of the field.
- Negative charges move in the opposite direction.
Electric Field Shielding
Conducting Surfaces and Shielding
- Conductors have a unique property: electric fields inside a conductor in electrostatic equilibrium are zero.
- This is because free electrons in the conductor rearrange themselves to cancel any external field.
- A hollow metal sphere placed in a strong electric field will have no electric field inside it.
- This is why sensitive electronic components are often shielded by metal casings.
How Shielding Works
- External Electric Field:
- When a conductor is placed in an external electric field, the field causes free electrons to move.
- Charge Redistribution:
- Electrons move until the internal field cancels the external field. This creates induced charges on the surface.
- Zero Internal Field:
- The result is that the electric field inside the conductor becomes zero.
This principle is used in Faraday cages, which protect sensitive equipment from external electric fields and electromagnetic interference.
- A common misconception is that the electric field inside a conductor is zero only if the conductor is solid.
- In reality, this applies to hollow conductors as well.
Magnet and Electromagnet
- How does the electric field strength change with distance in a radial field?
- What happens to the electric field inside a conductor in electrostatic equilibrium?
- How is the deflection of electrons controlled in a cathode ray tube?
