Question
A dipole placed in uniform electric field experiences:
Solution
An electric dipole consists of two point charges, +q and –q, separated by a small fixed distance 2a, with dipole moment p = q × 2a directed from –q to +q. When this dipole is placed in a uniform electric field E, each charge experiences an electric force: ● The positive charge experiences a force F = +qE in the direction of the field. ● The negative charge experiences a force F = –qE in the opposite direction. Since the electric field is uniform, the magnitudes of the forces on +q and –q are equal and opposite, and they act along parallel lines. Therefore: ● Net force on the dipole = 0
⇒ No translational motion (i.e., no linear acceleration). However, the two equal and opposite forces are separated by a distance, and hence form a couple, resulting in a torque τ on the dipole. The torque experienced by the dipole is given by:
τ = p × E
Or in scalar form:
τ = pE sinθ,
where θ is the angle between the dipole moment p and the electric field E. This torque tends to align the dipole along the direction of the electric field.
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2, 7, 19, 62, ?, 1270
4, 5, 11, 34, 137, ?
32 33 29 38 ? 47 11
...6848 + 9215 – 7295 - ? = 5945 – 3244
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100, 95, 85, 70, ?, 25 What will come in place of the question mark (?) in the following series?
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120, 126, 138, 162, ?, 306
-1, 5, 23, 59, ?
51 52 48 57 ? 66 30
...250, 279, 311, 349, 396, ?