Two short dipoles are placed perpendicularly as shown. Find electric field and potential at charge distance `r`.

Explanation

Electric field at `P`:
Due to `① , E_(1) = (1)/( 4 pi in_(0)) . ( 2p_(0))/(r^(3))`
Due to `②, E_(2) = (1)/( 4 pi in_(0)) . (2 p_(0))/(r^(3))`
`E_(p) = sqrt(E_(1)^(2) + E_(2)^(2)) = (1)/( 4pi in_(0)) (2 sqrt(2) p_(0))/(r^(3)) , theta = 45^(@)`
Electric potential at `P`:
Due to `① , V_(1) = (1)/( 4 pi in_(0)) . (p_(0))/(r^(2))`
Due to `②, V_(2) = 0`
`V_(p) = V_(1) + V_(2) = (1)/( 4pi in_(0)) . (p_(0))/(r^(2))`