CBSE Class 12 · 2008 · ElectrostaticsShort Answer

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Derive an expression for the torque acting on an electric dipole, which is held in a uniform electric field, when the axis of the dipole makes an angle

θ

with the electric field.

Answer: $τ = pE sin θ$ ; in vector form $τ = p \times E$ .

Solution

A dipole

(+ q, - q)

of separation

2 a

makes an angle

θ

with a uniform field

E

.
The charges feel forces

+ q E

and

- q E

— equal and opposite, so the net force is zero but they form a couple.
The perpendicular distance between their lines of action is

2 a sin θ

τ = (q E) (2 a sin θ) = (q \cdot 2 a) E sin θ

τ = pE sin θ, τ = p \times E

directed perpendicular to the plane of

p

and

E

CBSE Class 12 Board · 2008 · Subjective

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