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An electric dipole has a fixed dipole mo...

An electric dipole has a fixed dipole moment `vecp` which makes angle 9 with respect to X-axis. When subjected to an electric field `vecE_(1) = Ejhati` , it experience a torque `vecT_(1) = tauveck`When subjected to another electric field `vecE_(2) = sqrt(3)E_(1)hatj` it experiences a torque `vecT_(2) - vecT_(1)`. The angle `theta` is:

A

`60^(@)`

B

`90^(@)`

C

`30^(@)`

D

`45^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A

`vectau_(1) = vecp xx vecE`
`=(p_(x)hati + p_(y)hatj) xx Ehati`
`=-p_(y)Ehatk`………..(1)
and `vectau_(2) =(p_(x)hati + p_(y)hatj) xx sqrt(3)Ehatj`
`=sqrt(3)p_(x)Ehatk`………(2)
but `vectau_(2) =-vectau_(1)`
But `vectau_(2) =-vectau_(1)`
`therefore sqrt(3)p_(x)Ehatk =-(-p_(y)Ehatk)`
`therefore sqrt(3)=tan theta` (From figure)
`therefore theta = 60^(@)`
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