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

Step-by-step explanation:

It is given that,

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

Charge,
`q=2e=2* 1.6* 10^(-19)\ C=3.2* 10^(-19)\ C`

Distance between charges,
`d=0.82\ nm=0.82* 10^(-9)\ m`

Electric field strength,
`E=3.2* 10^6\ N/C`

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

`\tau=p* E\ sin\theta`

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

`\tau=p* 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* 10^(-19)* 0.82* 10^(-9)* 3.2* 10^6`

`\tau=8.39* 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.