Question

Derive the expression for couple acting on a electric dipole in a uniform electric field​

Answer 1

$\huge \underline \green{\sf{ Answer :- }}$

(1) A pair of opposite charges separated by a small distance is called dipole.

(2) Consider the charge of dipole are –q and +q coulomb and the distance between them is 2a.

(3) Then the electric dipole moment P is given by P = q × 2a = 2aq. It is a vector. It's direction is from –q to +q along the axis of dipole.

(4) It is placed in a uniform electric field E, making an angle θ with field direction as shown in fig.

(5) Due to electric field force on +q is F = +qE and force on –q is F = –qE.

(6) These two equal and opposite charges constitute torque or moment of couple. i.e.,

• torque, τ = ⊥r distance × magnitude of one of force
• ∴ τ = (2asinθ)qE = 2aqEsinθ = PEsinθ In vector form,
• τ = P x E

Answer 2

Answer:

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