The electric dipole is situated in an electric field as shown in figure. Both the dipole and the electric field are in the plane of the paper. The dipole is rotated about an axis perpendicular to the plane of the paper and passing through a point C. The direction of rotation is anticlockwise. If the angle of rotation θ is measured with reference to a line which is perpendicular to the electric field, then the variation of τ with θ is best represented by curve

Question

The electric dipole is situated in an electric field as shown in figure. Both the dipole and the electric field are in the plane of the paper. The dipole is rotated about an axis perpendicular to the plane of the paper and passing through a point C. The direction of rotation is anticlockwise. If the angle of rotation θ is measured with reference to a line which is perpendicular to the electric field, then the variation of τ with θ is best represented by curve (A) I (B) II (C) III (D) IV

Tardigrade Admin · Accepted Answer

vecτ= vecp × vecE=p E sin φ Where φ is the angle between vecp and vecE. Here, φ=90-θ ⇒ τ=p E sin (90-θ) τ=p E cos θ τ propto cos θ

I

II

III

IV

τ=p​×E=pEsinϕ Where ϕ is the angle between p​ and E. Here, ϕ=90−θ⇒τ=pEsin(90−θ) τ=pEcosθ τ∝cosθ

$τ = p \times E = pE sin ϕ$
Where $ϕ$ is the angle between $p$ and $E$ .
Here, $ϕ = 90 - θ \Rightarrow τ = pE sin (90 - θ)$
$τ = pE cos θ$
$τ \propto cos θ$