An electric dipole has a fixed dipole moment `vecp`, which makes angle `theta` with respect to x-aixs. When subjected to an electric field `vec(E)_(1)=Ehati`, it experiences a torque `vec(T)_(1)=tauhatk`. When subjected to another electric field `vec(E)_(2)=sqrt3Ehatj` it experiences a torque `vec(T)_(2)=-vec(T)_(1)`. The angle `theta` is

Options

A. `60^(@)`
B. `90^(@)`
C. `30^(@)`
D. `45^(@)`

Answer

A

Explanation

Here, `vec(tau_(2)) = -vec(tau_(1))`
From `vec(tau) = vec(p) xx vec(E)`

`vec(tau_(k)) - vec(tau_(k)) = (p_(x) hat(i) + p_(y) hat(j)) xx (E hat(i) xx sqrt(3) E hat(j))`
`= p_(x) xx sqrt(3) E hat(k) + p_(y) E (-hat(k))`
`0 = E hat(k) (sqrt(3) p_(x) - p_(y))`
or `(p_(y))/(p_(x)) = sqrt(3) i.e., tan theta = sqrt(3)`
`:. theta = 60^(@)`