D.2.3 Applications of electric and magnetic fields

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.

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:

$$E=\frac{V}{d}$$

Radial Fields

Fields Around Point Charges

1. A radial electric field is created by a point charge or a spherical conductor.
2. The field lines radiate outward from a positive charge and inward toward a negative charge.

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 ($8.99\times {10}^9{\text{N m}}^2{\text{C}}^{-2}$).

Deflection of Charged Particles

How Charged Particles Move in Electric Fields

1. Charged particles experience a force when placed in an electric field. This force causes them to accelerate.
2. The force ($F$) on a charge ($q$) in an electric field ($E$) is given by:

$$F=qE$$

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.

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.

How Shielding Works

1. External Electric Field:
   • When a conductor is placed in an external electric field, the field causes free electrons to move.
2. Charge Redistribution:
   • Electrons move until the internal field cancels the external field. This creates induced charges on the surface.
3. Zero Internal Field:
   • The result is that the electric field inside the conductor becomes zero.

Summary

1. Uniform Electric Fields: The electric field strength between parallel plates is given by $E=\frac{V}{d}$.
2. Radial Fields: The electric field around a point charge decreases with distance, following $E=\frac{kQ}{r^2}$.
3. Deflection of Charged Particles: Electric fields exert a force $F=qE$ on charged particles, causing them to accelerate.
4. Electric Field Shielding: Conductors eliminate electric fields inside them by redistributing charges on their surface.