Question

5. Derive an expression for the torque experienced by dipole due to a uniform electric field. ​

Answer 1

Consider an electric dipole of dipole moment → p placed in a uniform electric field → E whose field lines are equally spaced and point in the same direction. The charge +q will experience a force q → E in the direction of the field and charge -q will experience a force -q → E in a direction opposite to the field. Since the external field → E is uniform, the total force acting on the dipole is zero. These two forces acting at different points will constitute a couple and the dipole experience a torque. This torque tends to rotate the dipole. (Note that electric field lines of a uniform field are equally spaced and point in the same direction). The total torque on the dipole about the point O. Using right-hand corkscrew rule, it is found that total torque is perpendicular to the plane of the paper and is directed into it. The magnitude of the total torque where θ is the angle made by → p with → E . Since p = 2aq, the torque is written in terms of the vector product as → τ = → p x → E The magnitude of this torque is τ = pE sin θ and is maximum when θ =90°. This torque tends to rotate the dipole and align it with the electric field. Once → p is aligned with → E , the total torque on the dipole becomes zero.Read more on Sarthaks.com - https://www.sarthaks.com/889527/derive-an-expression-for-the-torque-experienced-by-a-dipole-due-to-uniform-electric-field

Answer 2

Answer :

these is the expression of torque.

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