For an electric dipole in a non-uniform electric field with dipole moment parallel to direction of the field, the force F and torque τ on the dipole respectively are ______.

Fill in the blank with the correct answer from the options given below.

The correct option is F ≠ 0, τ = 0.

1. Understanding the System:
An electric dipole consists of two equal and opposite charges, $-q$ and $+q$, separated by a small distance. The dipole moment vector $\mathbf{p}$ points from the negative charge to the positive charge. In this problem, the dipole is placed in a non-uniform electric field $\mathbf{E}$, and its dipole moment $\mathbf{p}$ is aligned parallel to the direction of the field.

2. Analysis of Torque ($\tau$):
The torque $\mathbf{\tau }$ acting on an electric dipole in an electric field is given by the cross product of the dipole moment and the electric field vector:
$\mathbf{\tau }=\mathbf{p}\times \mathbf{E}$
The magnitude of this torque is:
$\tau =pEsin\left(\theta \right)$
where $\theta$ is the angle between the dipole moment $\mathbf{p}$ and the electric field $\mathbf{E}$. Since the dipole moment is parallel to the direction of the field, the angle $\theta$ is $0°$. Since $sin(0°)=0$, the torque on the dipole is zero:
$\tau =0$

3. Analysis of Net Force ($F$):
In a uniform electric field, the forces on the positive and negative charges of the dipole are equal in magnitude and opposite in direction, leading to a net force of zero. However, in a non-uniform electric field, the electric field strength varies with position. As a result, the electric field at the position of the positive charge $+q$ is different from the electric field at the position of the negative charge $-q$:
${\mathbf{E}}_{+}\ne {\mathbf{E}}_{-}$
Consequently, the forces acting on the two charges, ${\mathbf{F}}_{+}=q{\mathbf{E}}_{+}$ and ${\mathbf{F}}_{-}=-q{\mathbf{E}}_{-}$, do not balance each other out. The net force on the dipole is:
$\mathbf{F}=q({\mathbf{E}}_{+}-{\mathbf{E}}_{-})\ne 0$
Thus, the net force $F$ acting on the dipole is non-zero ($F\ne 0$).

Conclusion:
Therefore, the dipole experiences a net non-zero translational force ($F\ne 0$) but experiences no rotational torque ($\tau =0$).