Derive an expression for torque acting on an electric dipole placed in a uniform electric filed (2M) - Physics - Magnetism and matter

Question

Derive an expression for torque acting on an electric dipole
placed in a uniform electric filed (2M)

Komal Jain · Accepted Answer

An electric dipole is placed in an uniform electric field as shown
in the figure

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"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/images/IMG-20140918-00374%20jpg"
style="width: 320px; height: 240px;">
The force on charge +q,FA→=qE→ along the direction of E→The force on charge -q,FB→=qE→ opposite to the direction of E→As these two forces are equal, unlike and parallel so they form a couple
AC is drawn perpendicular to E→
The perpendicular distance between the forces = arm of couple=ACtherefore, torque acting,τ=Force×Arm of couple⇒τ=F×ABsinθ⇒τ=qE×2asinθ⇒τ=(q×2a)Esinθ⇒τ=pEsinθ⇒τ=p→×E→

Derive an expression for torque acting on an electric dipole placed in a uniform electric filed. (2M)