A dipole is placed in an electric field as shown. In which direction will it move ?

Correct Option: towards the right as its potential energy will decrease.

Step-by-Step Explanation:

1. Analysis of the Diagram:
The setup consists of a source positive point charge, $+Q$, placed on the left side (at the origin). To the right of this source charge, an electric dipole is placed along the same axis. The dipole consists of a positive charge $+q$ on its left and a negative charge $-q$ on its right. Thus, the positive charge $+q$ is closer to the source charge $+Q$ than the negative charge $-q$ is.

2. Analysis of the Electric Field:
The electric field $E$ produced by a point charge $+Q$ at a distance $r$ is non-uniform and decreases with the square of the distance:

$E=\frac{1}{4\pi {\epsilon }_0}\frac{Q}{r^2}$

Since the positive charge $+q$ of the dipole is closer to the source charge $+Q$ (at distance $r_1$) than the negative charge $-q$ (at distance $r_2$, where $r_1<r_2$), the electric field is stronger at the position of the positive charge:

$E_1>E_2$

3. Calculating the Forces on the Charges:
The electrostatic force acting on a charge is given by the formula:

$F=qE$

Using this formula, we can evaluate the forces acting on the two charges of the dipole:
- The force on the positive charge $+q$ is a repulsive force directed away from the source charge, which points towards the right:
$F_{+}=q{E}_1$
- The force on the negative charge $-q$ is an attractive force directed towards the source charge, which points towards the left:
$F_{-}=q{E}_2$

4. Net Force and Direction of Motion:
Because the electric field is stronger at the closer position ($E_1>E_2$), the repulsive force to the right is stronger than the attractive force to the left:

$F_{+}>F_{-}$

This results in a net translational force acting on the dipole directed towards the right. As a result, the dipole will accelerate and move towards the right.

5. Potential Energy Change:
Any physical system naturally tends to move in the direction of the net conservative force to minimize its potential energy. The relationship between the net conservative force $F_{\text{net}}$ and the change in potential energy $dU$ is given by:

$dU=-F_{\text{net}}dx$

Since the dipole moves in the direction of the net force (towards the right, so $dx>0$ and $F_{\text{net}}>0$), the change in potential energy is negative ($dU<0$). This confirms that the potential energy of the dipole decreases as it moves to the right.