An electric dipole of length 1 cm is placed with the axis making an angle of 30° with an electric field of strength ${10}^4 N/C$. If it experiences a torque of  $10\sqrt{2}Nm$. The potential energy of the dipole when it maks an angle ${45}^0$ with the field is.   

 

Torque acting at any position is  $\tau =pE\sin \theta$  and potential energy at any position is U = -$pE\cos \theta$

Here in the first position  torque  $\tau = pE\sin {30}^0 = 10\sqrt{2}$  

Potential energy at  ${45}^0$  =  U = -pE cos${45}^0$

Dividing we get $\frac{\tau }{U}= \frac{pE \sin {30}^0}{pE \cos {45}^0}$   $\Rightarrow$$\mathrm{U} = \frac{10 \sqrt{2}\cos {45}^0}{\sin { 30}^0} =20 \mathrm{J}$