An electric dipole with electric dipole moment 4 ×10^-9 cm is aligned at 30^∘ with the directio

step 1 For this question, the magnitude of torque acting on the dipole is equal to PE sine theta. So th

An electric dipole with electric dipole moment 4 ×10^-9 cm...

An electric dipole with electric dipole moment $4 \times 10^{-9} \mathrm{~cm}$ is aligned at $30^{\circ}$ with the direction of a uniform electric field of magnitude $5 \times 10^{4} \mathrm{NC}^{-1}$. The magnitude of the torque acting on the dipole is (a) $10^{-6} \mathrm{Nm}$ (b) $10^{-4} \mathrm{Nm}$ (c) $10^{-10} \mathrm{Nm}$ (d) $10^{-2} \mathrm{Nm}$

An electric dipole with electric dipole moment $4 \times 10^{-9} \mathrm{~cm}$ is aligned at $30^{\circ}$ with the direction of a uniform electric field of magnitude $5 \times 10^{4} \mathrm{NC}^{-1}$. The magnitude of the torque acting on the dipole is
(a) $10^{-6} \mathrm{Nm}$
(b) $10^{-4} \mathrm{Nm}$
(c) $10^{-10} \mathrm{Nm}$
(d) $10^{-2} \mathrm{Nm}$

Key Concepts

Electric Dipole

An electric dipole consists of two equal and opposite charges separated by a small distance. It has a characteristic property called the dipole moment, which describes both the magnitude of the charges and the distance between them, and it provides information about how the dipole interacts with external electric fields.

Electric Dipole Moment

The electric dipole moment is a vector quantity defined as the product of the magnitude of one of the charges and the distance separating the charges. It indicates the strength of the dipole and the direction along which it acts, and is central to determining the dipole's behavior in an external electric field.

Uniform Electric Field

A uniform electric field has the same magnitude and direction at every point in space. This uniformity simplifies the analysis of forces and torques on objects like electric dipoles, as the field does not vary over the dipole's dimensions.

Torque on an Electric Dipole

When an electric dipole is placed in a uniform electric field, it experiences a torque that tends to align the dipole with the field. The torque is given by the product of the dipole moment, the electric field strength, and the sine of the angle between the dipole moment and the field. This relationship, ? = pE sin(?), is fundamental in understanding the rotational dynamics of dipoles in external fields.

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