When an electric dipole of moment `| vec(p) | = q xx 2a` is held at an angle `theta`, with the direction of uniform external electric field `vec(E)`, a torque `tau = pE sin theta` acts on the dipole. This torque tries to align the electric dipole in the direction of the field. When `vec(p)` is along `vec(E), theta^(@) , tau = pE sin 0^(@) = zero`. The dipole is in stabel equilibrium. The energy possessed by the dipole by virtue of its particular position in the electric field is called potential energy of dipole.
`U = W = -pE (cos theta_(2) - cos theta_(1))`
`theta_(1) = 90^(@)` is the position of zero potential energy.
` :. U = W = -pE (cos theta - cos 90^(@)) = -pE cos theta`.
For stable equillibrium, `theta 0^(@), :. U = -pE` = minimum.
Read the above passage and answer the following questions :
(i) What is the direction of torque acting on electric dipole held at an angle with uniform external electric field ?
(ii) An electric dipole of length 10cm having charges `+- 6xx10^(-3) C`, placed at `30^(@)` with respect to a uniform electric field experiences a torque of magnitude `6 sqrt(3) N-m`. Calculate.
(a) magnitude of electric field. (b) potential energy of dipole.
(iii) What is the physical significance of this concept in our day to day life ?

Explanation

To solve the given problem, we will break it down into the required parts and calculate the necessary values step by step.

### Given Data:
1. Length of the dipole, \( 2a = 10 \, \text{cm} = 0.1 \, \text{m} \) (therefore, \( a = 0.05 \, \text{m} \))
2. Charges of the dipole, \( q = 6 \times 10^{-3} \, \text{C} \)
3. Angle with respect to the electric field, \( \theta = 30^\circ \)
4. Torque experienced by the dipole, \( \tau = 6\sqrt{3} \, \text{N-m} \)

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