Electric Dipole Potential: Direction of Electric Field at Theta=0,45,90,135,180

[captainjack2000]

Homework Statement

The potential due to an electric dipole is V(r)=pcos(theta)/(4*PI*epsilon*r^2)
Determine the direction of the electric field E at theta = 0 , 45, 90, 135 and 180 degrees?

Homework Equations

The field of an electric dipole is given by Er = 2pcos(theta)/(4*PI*epsilon*r^3)
and E(theta) = psin(theta)/(4*PI*epsilon*r^3)

The Attempt at a Solution

I am a bit confused when look at the solutions to this question. For theta = 45 degrees is says that

" Er = 2*E(theta) = sqrt(2)*p/(4*PI*epsilon*r^3) or alternatively
Ez=p/(8*PI*epsilon*r^3) and E(x/y) = 3p/(8*PI*epsilon*r^3)
so E = sqrt(5/2)*p/(4*PI*epsilon*r^3)
at an angle to the dipole axis of alpha=72 degrees where tan(alpha)=3 "

I am unsure why Er = 2*E(theta) and how that arrived at the direction of the dipole (especially how they determined it to be at an angle of 72 degrees?? )

Thanks

 

[Doc Al]

I am unsure why Er = 2*E(theta)

Compare the formulas for E_r and E_θ for θ = 45 degrees. Realize that sin(45) = cos(45).

and how that arrived at the direction of the dipole (especially how they determined it to be at an angle of 72 degrees?? )

The are asking for the direction of the field with respect to the dipole direction, not the direction of the dipole.

Given that E_r = 2E_θ, first figure out (using a little trig) the angle the field makes with the radial direction (where θ = 45). The figure out its angle with respect to the dipole axis (which is where θ = 0).