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3.1.2.     Electric Field <CJ chap  18.6-18.8 >

3.1.2.1. Discussion

3.1.2.1.1.     Force at a distance was difficult for people to accept – thus the electric field, E, was ‘invented’

3.1.2.1.2.     The electric field at a point is the force a unit charge would experience. 

3.1.2.1.3.     E(x,y,z,t) is a vector field.  

3.1.2.1.4.     Electric field lines display E .  (E was at first an imaginary concept.)

3.1.2.1.5.     They can never cross.  They begin at + and end at – charges.

3.1.2.1.6.     E is zero inside a conducting material and excess resides on the surface.

3.1.2.1.7.     E just outside a conductor is always perpendicular to the conductor’s surface.

3.1.2.1.8.     Charge accumulates where the surface has the smallest radius of curvature.

3.1.2.1.9.     The electric field of a charged sphere shell is as though all charge is at its center (outside the sphere)

3.1.2.1.10.  The electric field of a charged spherical shell is zero (inside the sphere) - shielding

3.1.2.1.11.  Electric dipole is a pair of  equal but opposite charges separated by a distance

3.1.2.1.11.1.               Some molecules are dipolar such as water

3.1.2.1.11.2.               The electric field of a dipole is similar to that of a magnetic dipole (magnet)

3.1.2.1.12.  The electric field inside a parallel plate capacitor is uniform & often used as a source of an E field.

3.1.2.2. Mathematical

3.1.2.2.1.     Electric field equations

3.1.2.2.2.      E = F/q  =kq₀/r²     thus F = q E

3.1.2.2.3.     The electric field of a dipole (+ -), or ( + +) or (- -)

3.1.2.2.4.     Motion of a charged particle in a constant E field.  ma  = qE, use “constant a” formulas

3.1.2.2.5.     Electric dipole moment p is defined as p = Qd where +Q and –Q are a distance d apart

3.1.2.2.5.1. The electric dipole p is a vector pointing along d from the negative to the positive charge

3.1.2.2.5.2. An electric dipole feels a torque in an electric field of  t = p x E where t is a vector

3.1.2.2.5.3. An electric dipole in a field E has an energy of U = - p  E where U is a scalar

3.1.2.3. Advanced

3.1.2.3.1.     Vector expression of the electric field

3.1.2.3.2.     E(r) = k  q₁ (r-r₁) / |r-r₁|³   where  E and r are vectors

3.1.2.3.3.     Generally the Electric field from charges q_i is  E_q (r) = S_i q_i (r-r_i) / |r-r_i|³   

3.1.2.3.4.     Vector problems