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CBSE Class 12 Physics 2014 Delhi Set 1 Paper

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Question : 16 of 30
Marks: +1, -0
An electric dipole of length 4 cm4\ \text{cm}, when placed with its axis making an angle of 60∘60^{\circ} with a uniform electric field, experiences a torque of 4 3 Nm4\ \sqrt{3}\ \text{Nm}. Calculate the potential energy of the dipole, if its has charge ±8 nC\pm 8\ \text{nC}.
Solution:  
τ  =p E sin⁡  θ\tau\;=p\ E\ \sin\;\theta
4 3  =p E sin⁡  θ4\ \sqrt{3}\;=p\ E\ \sin\;\theta
p E  32  =4 3p\ E\;\frac{\sqrt{3}}{2}\;=4\ \sqrt{3}
So,     p E=8\;\;p\ E=8
Potential energy of the dipole =−p E cos⁡θ=-p\ E\ \cos\theta
  U=−p E cos⁡60\;U=-p\ E\ \cos 60
  U=−8 × 0.5\;U=-8\ \times\ 0.5
  U=−4 J\;U=-4\ \text{J}
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