Question

two short electric dipoles P1 and P2 are placed at an angle θ and r is the distance between their centres. The energy of electric interaction between these dipoles will be: (C is the centre of dipole moment P2)
1. 2k P1 P2 cos θ/r^3
2. -2k P1 P2 cos θ/r^3
3. -2k P1 P2 sin θ/r^3
4. -4k P1 P2 cos θ/r^3

Answer 1

unable to understand. Plz write property

Answer 2

Answer:

The correct answer is option 2 $\frac{-2 k P_{1} P_{2} \cos \theta}{r^{3}}$

Explanation:

Given two short electric dipoles which are inclined at an angle θ with each other. They have some potential energy due to their mutual interaction. Therefore apply the basic formula of the potential energy of the dipoles but while substituting the values, we must take care of the orientation of the two dipoles with respect to each other.

The potential energy of interaction of dipoles, $U$ is expressed as:

$U=-\frac{2 k P_{1} P_{2}}{r^{3}}$

Where,

$k=\frac{1}{4 \pi \varepsilon_{0}} and \varepsilon_{0}=8.85 \times 10^{-12} \mathrm{Fm}^{-1} \\and is called the permittivity of free space$

$\Rightarrow k=9 \times 10^{9}$

$P_{1}=$ dipole moment of one dipole

$P_{2}=$ dipole moment of second dipole

$r=$ distance between the dipole and the position vector

Here, those component dipole moments must be taken which is parallel to the position vector of the dipole.

The vertical component of dipole $P_{1}$ becomes equal to zero and the horizontal component is

considered further. Therefore, we shall the dipole moments as $P_{1} \cos \theta$and $P_{2}$ because the two dipoles are inclined at angle $\theta$ with each other.

Thus, substituting the values, we get

$\begin{aligned}&U=-\frac{2 k P_{1} \cos \theta P_{2}}{r^{3}} \\&\Rightarrow U=-\frac{2 k P_{1} P_{2} \cos \theta}{r^{3}}\end{aligned}$