Question

derive an expression for the torque acting on an electric dipole which is held in a uniform field when the axis of the dipole make angle ∅ with electric field​

Answer 1

Answer:

$\Large{\underline{\underline{\bf{Given:}}}}$

• Electric dipole is in uniform electric field
• Dipole makes angle θ with electric field

$\Large{\underline{\underline{\bf{To\:Find:}}}}$

• Expression for torque acting on the dipole

$\Large{\underline{\underline{\bf{Solution:}}}}$

→ Consider a dipole which is placed in a uniform electric field at points A and B. The distance between them is 2a.

→ Force will be experienced by both positive and negative charges

→ F = q E

→ F₁ = Force due to positive charge = +q E which acts in the opposite direction of electric field.

→ F₂ = Force due to negative charge = -q E which acts in the same direction of electric field.

→ The net force on the system = F₁ +  F₂ = +q E - q E = 0

→ Here both forces are equal in magnitude and acts in the opposite direction on different points. Hence it acts a couple and starts to rotate which produces torque

→ Torque ($\tau$) = One of the forces which produces rotating effect × Perpendicular distance of the force.

$\tau$ = q E × OB------equation 1

→ Consider ΔBAO

   sin θ = OB/AB

   OB = AB sinθ

   OB = 2a sinθ

→ Put the value of OB in equation 1

$\tau$ = q E × 2a sinθ

→ But dipole moment (p) = 2a × q

  $\tau$ = p E sin θ