The Electric Field
- Forces - Coulomb's Law
- Contact Forces
- Intuitive
- Action-at-a-distance
- Electric Field
- Proposed by Michael Faraday
- Electric field surrounds charge
- Second charge interacts with the field
- Field independent of second charge
- related to size of force on 2nd charge
- but independent of second charge
- Vector Quantity
- need magnitude and direction
- Magnitude
- Direction of E
- Direction determined by the motion of a positive test charge
- (+) charge will have field pointing away from it
- (-) charge will have field pointing toward it
- Problem
- new charge can affect the original distribution
- affects the field
- Solution
- make test charge sufficiently small
- Representing the Electric Field (1)
- Draw Arrows representing Motion of test charge
- arrow points in direction of field
- length of arrow depends on field size
- Representing the Electric Field (2)
- Connect Arrows to produces field lines
- lines tangent to electric field
- # of lines proportional to electric field
- field lines cannot cross
- field lines begin on + charge or at infinity
- field lines end on - charge or at infinity
- Examples
- Finding the Electric Field for Multiple Charges
- Electric field obey superposition (as they must - think about it)
- to find the electric field at a point due to multiple charges
- What happens if the charges are not discrete but continuous
- break distribution into little chunks
- how small should the pieces be - as small as possible
- limiting case - size of charges approaches zero
- r represents the distance from the charge to the field point, unit vector r
points away from the charge, dq represents a little piece of charge
- if the charge is distributed over a volume
- if the charge is distributed over an area
- if the charge is distributed along a line
- Examples
- Motion of a Charged Particle in Uniform Electric Field
- Force on charged particle: F = qE
- Newton's Second Law: F = ma
- a = qE/m ( constant acceleration)
- Equations of Kinematics apply to describe motion
- similar to particle in gravitational field with g replaced by qE/m
- motion depends on the charge and mass
- Conductors (in electrostatic equilibrium)
- Electric Field is zero in conductor.
- Any excess charge is all on surface.
- Electric field is perpendicular to surface
- Charge will accumulate at sharp points
