The given problem involves a dipole placed in an electric field. To determine the direction in which the dipole will move, we need to consider the behavior of a dipole in an electric field.
When a dipole is placed in an electric field, the dipole experiences a torque that tends to align it with the field. The potential energy of the dipole in an electric field is given by:
U = -p · E
Where:
The dipole will move towards the direction where its potential energy decreases. This happens when the dipole rotates to align with the electric field, minimizing its potential energy.
In this case, as the dipole aligns with the electric field, it moves towards the right, where the potential energy is lower.
Final Answer:
The dipole will move towards the right as its potential energy will decrease.
The center of a disk of radius $ r $ and mass $ m $ is attached to a spring of spring constant $ k $, inside a ring of radius $ R>r $ as shown in the figure. The other end of the spring is attached on the periphery of the ring. Both the ring and the disk are in the same vertical plane. The disk can only roll along the inside periphery of the ring, without slipping. The spring can only be stretched or compressed along the periphery of the ring, following Hooke’s law. In equilibrium, the disk is at the bottom of the ring. Assuming small displacement of the disc, the time period of oscillation of center of mass of the disk is written as $ T = \frac{2\pi}{\omega} $. The correct expression for $ \omega $ is ( $ g $ is the acceleration due to gravity): 
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
An electric dipole is a pair of equal and opposite point charges -q and q, separated by a distance of 2a. The direction from q to -q is said to be the direction in space.
p=q×2a
where,
p denotes the electric dipole moment, pointing from the negative charge to the positive charge.
