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## 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