Orientation Polarization Decay After Field Removal A polar liquid contains N permanent dipoles of moment μp per unit volume. After a long DC field application, the orientation polarization equals P0. At time t = 0 the field is suddenly removed. What happens to the polarization P(t)?
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AIt will remain constant at P0 for all time
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BIt becomes zero instantaneously at t = 0
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CIt decays toward zero with a characteristic time constant
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DEither (b) or (c), depending on the initial field strength
Answer
Correct Answer: It decays toward zero with a characteristic time constant
Explanation
Introduction / Context:In dielectrics with permanent dipoles (polar liquids), an applied electric field partially aligns the dipoles, producing orientation polarization. When the field is removed, thermal agitation randomizes orientations again. The kinetics of this relaxation are classically described by a first-order (Debye) process with a characteristic relaxation time τ.
Given Data / Assumptions:
- Permanent dipoles of density N and moment μp.
- Steady orientation polarization P0 reached under a DC field.
- At t = 0 the field is set to zero; linear, isothermal response.
Concept / Approach:
Debye theory models rotational diffusion in a viscous medium, leading to exponential relaxation of polarization after a step change in the field. After removal, the driving torque vanishes and randomizing collisions cause P(t) to decay from P0 to 0 with time constant τ that depends on viscosity, temperature, and molecular size.
Step-by-Step Solution:
Model polarization dynamics as dP/dt = −(P/τ) after field removal.Integrate: P(t) = P0 * exp(−t/τ).As t → ∞, P(t) → 0; at t = 0+, P is continuous (no instantaneous drop to 0).Verification / Alternative check:
Dielectric relaxation spectroscopy measures frequency-dependent permittivity; the time-domain equivalent shows exponential decay following a field step, confirming the Debye-type response.
Why Other Options Are Wrong:
- Constant P0 contradicts thermal randomization once the aligning field is removed.
- Instantaneous zero would imply infinite relaxation rate, unphysical for molecular rotations.
- Dependence on initial field strength does not change the qualitative exponential decay for linear response.
Common Pitfalls:
Confusing electronic/atomic polarization (nearly instantaneous) with orientation polarization (viscous, time-dependent); assuming non-causal jumps in macroscopic polarization.
Final Answer:
It decays toward zero with a characteristic time constant