a the dipole is parallel to the electric field b the dipole

(a) the dipole is parallel to the electric field,

(b) the dipole is perpendicular to the electric field, and

(d) Find the potential energy of the dipole in the electric field for each case.

The torque on an electric dipole is given by

tau = pxE

potential energy of dipole is given by

U = -p.E

A. tau at theta = 0 deg

tau = pE*sin A = pE*sin 0 = 0

B. at theta = 90 deg

tau = 0.5*1.6*10^-19*10^-9*3*10^4*sin 90 = 2.4*10^-24 N-m

C. at theta = 30 deg

tau = 0.5*1.6*10^-19*10^-9*3*10^4*sin 30 = 1.2*10^-24 N-m

D. U = -pE*cos A

i. U = -pE*cos 0 = -0.5*1.6*10^-19*10^-9*3*10^4*cos 0 = -2.4*10^-24 J

ii. U = -0.5*1.6*10^-19*10^-9*3*10^4*cos 90 = 0 J

iii. U = -0.5*1.6*10^-19*10^-9*3*10^4*(cos 30 deg) = -2.078*10^-24 J