Dipoles

Question 1

dipole equation

Answer 1

p = qd
p: dipole
q: charge of one of the charges in the dipole
d: seperation

Question 2

torque of a dipole in an electric field

Answer 2

T = p X E
T: torque (tau symbol)
p: dipole
E: electric field
X: cross product

Question 3

energy of a dipole in an electric field

Answer 3

U = -p⋅E
U: energy
p: dipole
E: electric field
⋅ : dot product

Question 4

potential at a point r from a dipole

Answer 4

ϕ = [Qd*cos(θ) ]/4πr²ε₀
θ: angle between d and r
d: dipole length (separation of the charges)
r: distance from the centre of the dipole

Question 5

general E-field equation for a dipole

Answer 5

E =[Qd/4πε₀r³] * [2cos(θ) + sin(θ)]

the 2cos(θ) is in the r hat direction and the sin(θ) is in the theta hat direction

Question 6

what is a dipole

Answer 6

dipoles form when 2 equal and opposite charges are separated by a small displacement, d. Some molecules have permanent electric dipoles

Question 7

how would you get the general E-field from a dipole

Answer 7

ϕ = Qdcos(θ)/4πr²ε₀
and E = -∇ϕ

remember ∇ϕ = ∂ϕ/∂r ŕ +1/r[∂ϕ/∂θ] θ(hat)

this gives:
E =[Qd/4πε₀r³] * [2cos(θ) + sin(θ)]

the 2cos(θ) is in the r hat direction and the sin(θ) is in the theta hat direction