(a) An electric dipole with dipole moment p⃗ is placed at an angle θ with respect to a uniform electric field E⃗. Determine the torque acting on the dipole and write its vector form. (b) Two charges of magnitude +q and +4q are held fixed on the X-axis at a mutual separation of 'd

Question

(a) An electric dipole with dipole moment p⃗ is placed at an angle θ with respect to a uniform electric field E⃗. Determine the torque acting on the dipole and write its vector form. (b) Two charges of magnitude +q and +4q are held fixed on the X-axis at a mutual separation of 'd'. Where should a third charge of magnitude +2q be placed so that it experiences no net force? ((2+1)+2)

**OR**

(a) Two similar large plane plates, each of area 'A', are placed in air at a distance 'd' from each other, with surface charge densities +σ and –σ respectively. (i) Determine the expression for the electric field at a point between the two plates. (ii) Determine the potential difference between the two plates. (iii) Determine the capacitance of the capacitor formed by the two plates. (b) Calculate the effective capacitance of the capacitor combination shown below. ((1+1+1)+2)

Accepted Answer

>

> [!TLDR]
> The torque on a dipole is τ⃗ = p⃗ × E⃗ (magnitude pE sinθ); and by balancing the Coulomb forces from +q and +4q, the null point for +2q lies between them, at d/3 from the +q charge.
>
> **(a) Torque on a dipole:** An electric dipole of moment p⃗ placed in a uniform field E⃗, making angle θ with it, experiences equal and opposite forces (qE) on its two charges, separated by the dipole length, forming a couple. The magnitude of this torque is
> $$	au = pE\sin	heta$$
> and in vector form,
> $$\vec	au = \vec p 	imes \vec E$$
> (There is no net force on the dipole in a uniform field, only this torque, which tends to align p⃗ with E⃗.)
> …

Q.(a) An electric dipole with dipole moment p⃗ is placed at an angle θ with respect to a uniform electric field E⃗. Determine the torque acting on the dipole and write its vector form.

Concept understanding — Electric Dipole in a Field

Electric Dipole in a Uniform Field — First Look

What happens? Two forces, one twist

The torque formula

What does this mean physically?

Q.(a) An electric dipole with dipole moment p⃗ is placed at an angle θ with respect to a uniform electric field E⃗. Determine the torque acting on the dipole and write its vector form.

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