Electric Charges and Electric Fields

Introduction to Electric Fields

• Consider a single charge, ( q ), in space.
• If another charge is placed near ( q ), it experiences a force due to ( q ).
  • Like charges repel; opposite charges attract.
• This interaction can be described using the concept of an electric field.
• An electric field is a way to describe the influence a charge exerts on the space around it.

Coulomb's Law

• The force ( F ) between two point charges is expressed as:

  [ F = k \frac{Q \cdot q}{r^2} ]

  • ( k ) is Coulomb's constant ( (9 \times 10^9 , \text{Nm}^2/\text{C}^2) ).
  • ( Q ) is the charge creating the field.
  • ( q ) is the test charge placed in the field.
  • ( r ) is the distance between the charges.

Electric Field Definition

• The electric field ( E ) at a point is defined as the force per unit charge:

  [ E = \frac{F}{q} = k \frac{Q}{r^2} ]

• ( E ) is measured in Newtons per Coulomb (N/C).

• ( E ) is a vector field, indicating both magnitude and direction.

Calculating Electric Field

• Example: Calculate ( E ) 2 meters away from a ( 1 \times 10^{-6} , \text{C} ) charge.

  [ E = k \frac{Q}{r^2} = 9 \times 10^9 \times \frac{1 \times 10^{-6}}{2^2} = 2500 , \text{N/C} ]

Force on a Test Charge

• To find force ( F ) on a ( 1 \text{ C} ) test charge placed 2 meters from ( Q ):

  [ F = qE = 1 \times 2500 = 2500 , \text{N} ]

• Direction is outward for repulsion, inward for attraction.

Visualizing Electric Fields

• Electric field lines indicate the path a positive test charge would follow.
  • Lines radiate outwards from positive charges, inwards to negative charges.
• Density of lines indicates field strength:
  • Closer lines = stronger field.
  • Lines spread out = weaker field.

Example Problem

• Force on an electron in an electric field ( E = 100 , \text{N/C} ):

  [ F = q \times E = -1.6 \times 10^{-19} \times 100 = -1.6 \times 10^{-17} , \text{N} ]

Key Concepts

• Electric fields help visualize and quantify the spatial influence of charges.
• Field strength decreases with distance from the charge.
• Field lines provide a visual representation of field strength and direction.