Why does the torque become unstable at 180 degree, when a dipole is pl...
**Introduction**
When a dipole is placed in a uniform electric field, it experiences a torque due to the interaction between the electric field and the dipole moment. The torque tends to align the dipole moment with the electric field, resulting in stable equilibrium. However, at 180 degrees, the torque becomes unstable, causing the dipole to rotate.
**Explanation**
1. **Dipole in an Electric Field**: A dipole consists of two equal and opposite charges separated by a distance. When placed in a uniform electric field, the charges experience forces in opposite directions. The force on one charge is stronger than the other, leading to a net force acting on the dipole.
2. **Torque on a Dipole**: The torque on a dipole in an electric field is given by the equation: τ = pEsinθ, where τ is the torque, p is the dipole moment, E is the electric field strength, and θ is the angle between the dipole moment and the electric field.
3. **Stable Equilibrium**: When the dipole is aligned with the electric field (θ = 0 degrees), the torque is zero. This corresponds to stable equilibrium, as there is no rotational tendency. The dipole remains in this position unless disturbed.
4. **Unstable Equilibrium**: At 180 degrees (θ = 180 degrees), the torque becomes maximum. This occurs because the sine of 180 degrees is also maximum (sin180 = 1). The torque is given by τ = pEsinθ = pEsin180 = pE. The dipole experiences a maximum rotational tendency to align itself with the electric field.
5. **Rotational Motion**: When the dipole is slightly displaced from the stable equilibrium position (θ ≠ 0), the torque acts to restore the dipole to its stable position. However, when the dipole is displaced from the unstable equilibrium position (θ ≠ 180 degrees), the torque acts to further rotate the dipole away from the unstable position.
6. **Energy Considerations**: At 180 degrees, the dipole has maximum potential energy (U = -pEcosθ). Any deviation from this position results in a decrease in potential energy, driving the dipole to rotate away from the unstable equilibrium.
7. **Dynamic Equilibrium**: The dipole oscillates back and forth around the stable equilibrium position due to the torque. It does not settle at 180 degrees due to the unstable nature of that equilibrium.
In conclusion, the torque becomes unstable at 180 degrees when a dipole is placed in a uniform electric field due to the maximum rotational tendency and the associated increase in potential energy. This causes the dipole to rotate away from the unstable equilibrium position.
Why does the torque become unstable at 180 degree, when a dipole is pl...
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