Physics

Physics

Problem

A charge +Q+Q is fixed at the origin of the co-ordinate system while a small electric dipole of dipole moment p⃗\vec{p} pointing away from the charge along the xx-axis is set free from a point far away from the origin. a. Calculate the K.E. of the dipole when it reaches to a point (d,0)(d, 0) . b. Calculate the force on the charge +Q+Q at this moment.
Intuitive explanation

The key is recognizing that a dipole in a non-uniform electric field experiences both a force (pulling it toward regions of stronger field) and a torque (aligning it with the field). Since the charge +Q+Q creates a radial field that weakens with distance, the dipole will be attracted inward and simultaneously experience a torque trying to align p⃗\vec{p} with the field direction. Use energy methods—the interaction energy U=−p⃗⋅E⃗U = -\vec{p} \cdot \vec{E} combined with the dipole's initial orientation and the field geometry—to find the motion without solving complicated force equations directly.

Intuitive explanation

The key is recognizing that a dipole in a non-uniform electric field experiences both a force (pulling it toward regions of stronger field) and a torque (aligning it with the field). Since the charge +Q+Q creates a radial field that weakens with distance, the dipole will be attracted inward and simultaneously experience a torque trying to align p⃗\vec{p} with the field direction. Use energy methods—the interaction energy U=−p⃗⋅E⃗U = -\vec{p} \cdot \vec{E} combined with the dipole's initial orientation and the field geometry—to find the motion without solving complicated force equations directly.

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