Electric Field due to a Point Charge q

	Magnitude: Direction: Radially outwards for positive charges and radially inward for negative charges.
	Derived from Coulomb's Law

• For a set of charges, the total E-fiels is the vector sum of the E-field of each charge.

Electric Field due to a Infinite Line Charge with Uniform Charge Density l

l = Charge per unit length (SI: C/m) Derivation Magnitude: Direction: Radially outwards for a positive l, perpendicular to the line charges.

It is assumed that the charges on the line are fixed in position. A conduction rod would produce just an E-field, but as soon as you put any charge near the rod, the distribution of charge on the rod would change.

Electric Field on the Axis of a Charged Ring with a Uniform Charge Density

Q = Total Charge on the Ring of radius R Derivation Magnitude: Direction: Outwards away from the ring along the axis of the ring if Q is positive.

• The ring is assumed to lie in zy-plane with its axis along the x-axis

• The E-field (as a function of its location) at points other than along the axis is very complex and it can not easily be expressed by such a simple function.

Electric Field due to Infinitely Flat, Charged-Plane with a Uniform Charge Density

s = Charge per unit area on the plane (SI: C/m 2) Derivation Magnitude: Direction: Outwards perpendicular to the plane.

• For an infinite sheet the E-field is the same at any distance from the sheet, i.e. the E-field is constant.
  
  
• This expression is useful for electrical conductors because the charge spreads out on the conductor's surface forming a surface charge distribution s. Although the charge density s is not necessarily constant over the surface, but if you get close enough, the conductor's surface will look like a infinitely charge sheet. The electric field will be perpendicular to the surface and equal to half of a charged sheet because the E-field inside the conductor is zero.