Question

An electric dipole consists of charges +2e and -2e separated by 0.82 nm. It is in an electric field of strength 3.2 x 10^6 N/C. Calculate the magnitude of the torque on the dipole when the dipole moment is (a) parallel to, (b) perpendicular to, and (c) antiparallel to the electric field

Answer 1

Explanation:

It is given that,

An electric dipole consists of charges +2e and -2e separated by 0.82 nm

Charge, $q=2e=2\times 1.6\times 10^{-19}\ C=3.2\times 10^{-19}\ C$

Distance between charges, $d=0.82\ nm=0.82\times 10^{-9}\ m$

Electric field strength, $E=3.2\times 10^6\ N/C$

(a) The magnitude of the torque on the dipole is given by :

$\tau=p\times E\ sin\theta$

When dipole moment is parallel to the electric field, $\theta=0$

$\tau=p\times E\ sin(0)$

$\tau=0$

(b) When the dipole is perpendicular to the electric field, $\theta=90$

$\tau=pE\ sin(90)$

$\tau=qdE$ (Since, p = q × d)

$\tau=3.2\times 10^{-19}\times 0.82\times 10^{-9}\times 3.2\times 10^6$

$\tau=8.39\times 10^{-22}\ N.m$

(c) When the dipole moment is anti parallel to the electric field, $\theta=180$

$\tau=pE\ sin(180)$

Since, $sin\ 180=0$

$\tau=0$

Hence, this is the required solution.