Physics · Electric field: electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in a uniform electric field
There exists a non-uniform electric field along -axis as shown in the figure bel
There exists a non-uniform electric field along \( x \) -axis as shown in the figure below. The field increases at a uniform rate along +ve x-axis. A dipole is placed inside the field as shown.Which one of the following is correct for the dipole?
- A. Dipole moves along positive x-axis and undergoes a clockwise rotation
- B. Dipole moves along negative x-axis and undergoes a clockwise rotation
- C. Dipole moves along positive x-axis and undergoes a anticlockwise rotation
- D. Dipole moves along negative x-axis and undergoes a anticlockwise rotation
Step-by-step solution
The field increases uniformly along the +x direction, so the gradient dE/dx > 0. For a dipole with moment p having a positive x-component (p_x > 0), the net force F = p_x (dE/dx) i is in the +x direction, causing translation to the right. The torque τ = p × E tends to align the dipole with the field. With the dipole oriented as typically shown (moment in the first quadrant, above the x-axis), the torque is clockwise (into the page) to reduce the angle, resulting in clockwise rotation. Thus, the dipole moves right and rotates clockwise.
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