An electric dipole in a constant external electric field has net force zero on it. This means

CONCEPT:

Electric dipole:

• When two equal and opposite charges are separated by a small distance then this combination of charges is called an electric dipole.
• The strength of an electric dipole is measured by a quantity known as a dipole moment i.e.

\(\vec P = q \times \overrightarrow {2a} \)

Where q = charge and 2a = distance between two charged particles

• The electric dipole moment is denoted by P and the SI unit of dipole moment is coulombmeter (Cm).

EXPLANATION:

• Let this dipole be placed in a uniform electric field E at an angle θ with the direction of E.
• Force on charge +q at A = qE, along the direction of E and force on a charge -q at B = qE, along the direction opposite to E.
• Since the electric field (E) is uniform, therefore, the net force on the dipole is 0.
• The net force on the electric dipole in a constant electric field is always zero. Therefore option 4 is correct

Additional Information

• However, as the forces are equal, unlike and parallel, acting at different points, therefore, they form a couple which rotates the dipole. Hence, the couple tends to align the dipole along the direction of the electric field (E).

⇒ τ = force × arms of a couple

⇒ τ = F × 2asinθ = (qE) × 2asinθ

⇒ τ = (q × 2a)E sinθ \(\vec{\tau }=\vec{p}\times ~\vec{E}\)

⇒ τ = pE sinθ