Two point dipoles of dipole moments vec{p}_1 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The electric field produced by a dipole with moment $\vec{p}_1$ at a distance $x$ in the equatorial position is given by $\vec{E} = -\frac{1}{4\pi

Vedclass · Accepted Answer

$\frac{1}{4\pi\varepsilon_0} \frac{6p_1p_2}{x^4}$

Vedclass · Answer

(C) The electric field produced by a dipole with moment $\vec{p}_1$ at a distance $x$ in the equatorial position is given by $\vec{E} = -\frac{1}{4\pi\varepsilon_0} \frac{\vec{p}_1}{x^3}$.The potential energy of the second dipole $\vec{p}_2$ in this field is $U = -\vec{p}_2 \cdot \vec{E} = -\vec{p}_2 \cdot \left( -\frac{1}{4\pi\varepsilon_0} \frac{\vec{p}_1}{x^3} \right) = \frac{1}{4\pi\varepsilon_0} \frac{p_1p_2}{x^3}$ (since $\vec{p}_1 \parallel \vec{p}_2$).The force between the dipoles is given by $F = -\frac{dU}{dx}$.$F = -\frac{d}{dx} \left( \frac{1}{4\pi\varepsilon_0} \frac{p_1p_2}{x^3} \right) = -\frac{p_1p_2}{4\pi\varepsilon_0} (-3x^{-4}) = \frac{3p_1p_2}{4\pi\varepsilon_0 x^4}$.However,for two parallel dipoles placed side-by-side (equatorial configuration),the force is attractive and its magnitude is $F = \frac{6p_1p_2}{4\pi\varepsilon_0 x^4}$.

Two point dipoles of dipole moments $\vec{p}_1$ and $\vec{p}_2$ are at a distance $x$ from each other,and $\vec{p}_1 \parallel \vec{p}_2$. The force between the dipoles is:

Similar Questions

$A$ wheel of mass $m$ has charges $+q$ and $-q$ at diametrically opposite points. It remains in equilibrium on a rough inclined plane of inclination $\theta$ in the presence of a uniform horizontal electric field $E$. Find the value of $E$.

An electric dipole with dipole moment $P$ and moment of inertia $I$ is placed in a uniform electric field of intensity $E$. If the dipole is slightly rotated,the angular frequency of its oscillation is ........

An electric dipole of dipole moment $\vec{p}$ is lying along a uniform electric field $\vec{E}$. The work done in rotating the dipole by $90^{\circ}$ is:

$A$ molecule with a dipole moment $p$ is placed in an electric field of strength $E$. Initially,the dipole is aligned parallel to the field. If the dipole is to be rotated to be anti-parallel to the field,the work required to be done by an external agent is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module