Q.A charged particle has drift velocity 4.2 x 10^-4 m s^-1 in electric field of 2.1 x 10^-10 V m^-1. Its mobility is

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1. CBSE 2026Set ANNUAL1 mark
   Q.What is the S.I. unit of mobility (mu)?

   ›Reveal solutionSolution

   Mobility is drift velocity per unit electric field, so its unit works out to m^2/(V.s).

   Mobility mu of a charge carrier is defined as the drift velocity acquired per unit applied electric field:

   mu = vd / E

   …

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2. CBSE 2025Set ANNUAL1 mark
   Q.Magnitude of the drift velocity per unit electric field is equal to ____________.

   ›Reveal solutionSolution

   Drift velocity per unit applied field is, by definition, the mobility of the charge carriers.

   When an electric field $E$ is applied across a conductor, free charge carriers acquire an average drift velocity $v_d$ proportional to $E$ (for ohmic conductors):

   $v_d = \mu E \quad \Rightarrow \quad \mu = \dfrac{v_d}{E}$

   …

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3. CBSE 2025Set ANNUAL1 mark
   Q.How does the mobility of electron in a conductor change, if the potential difference applied across the conductor is double keeping the length and temperature of the conductor constant?

   ›Reveal solutionSolution

   Mobility $\mu = e\tau/m$ depends only on the material, not on the applied field; $v_d=\mu E$ changes, $\mu$ does not.

   …

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4. CBSE 2024Set ANNUAL1 markMCQ
   Q.The SI unit of mobility ($\mu$) of charge carriers is -

   (a) $m^2V^{-1}$

   (b) $m^2V^{-1}s^{-1}$

   (c) $m^2Vs$

   (d) $m^2V^2s$

   ›Reveal solutionSolution

   Mobility is drift velocity per unit electric field, so its unit works out to $m^2V^{-1}s^{-1}$.

   Mobility $\mu = v_d/E$, where $v_d$ is drift velocity (unit $ms^{-1}$) and $E$ is electric field (unit $Vm^{-1}$). So the SI …

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5. CBSE 2024Set ANNUAL1 mark
   Q.The magnitude of drift velocity of electron per unit electric field is called __________.

   ›Reveal solutionSolution

   Mobility is defined precisely as drift speed per unit electric field, and characterises how easily charge carriers drift under a field.

   When an electric field E is applied across a conductor, free electrons acquire an average drift velocity $v_d$ superimposed on their random thermal motion. The quantity:

   $\mu = \dfrac{v_d}{E}$

   …

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6. CBSE 2023Set ANNUAL1 markMCQ
   Q.A charged particle has drift velocity 4.2 x 10^-4 m s^-1 in electric field of 2.1 x 10^-10 V m^-1. Its mobility is

   (1) 0.5 x 10^6 m^2 V^-1 s^-1

   (2) 2 x 10^6 m^2 V^-1 s^-1

   (3) 0.5 x 10^-6 m^2 V^-1 s^-1

   (4) 2 x 10^-6 m^2 V^-1 s^-1

   ›Reveal solutionSolution

   Mobility is the drift velocity acquired per unit electric field.

   …

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7. CBSE 2022Set GC1 mark
   Q.Define mobility.

   ›Reveal solutionSolution

   Mobility $\mu=v_d/E$ — drift velocity per unit applied electric field.

   Definition. The mobility of a charge carrier is the magnitude of the drift velocity it acquires per unit electric field applied across the conductor:

   $\mu=\frac{v_d}{E}.$ …

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8. CBSE 2022Set I1 markMCQ
   Q.Which of the following is correct for mobility? (A) μ = V_d/E (B) μ = E/V_d (C) μ = V_d·E (D) μ = E^2·V_d

   ›Reveal solutionSolution

   Mobility μ = drift velocity per unit field = V_d/E.

   Mobility measures how readily charge carriers drift in an applied electric field. It is defined as the magnitude of drift velocity per unit electric field:

   $\mu = \dfrac{v_d}{E}$

   …

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9. CBSE 2022Set ANNUAL1 mark
   Q.Magnitude of the drift velocity per unit electric field is ____.

   ›Reveal solutionSolution

   The drift velocity acquired per unit applied electric field is the mobility of the charge carrier.

   When an electric field E is applied across a conductor, free electrons acquire a small average velocity along the field called the drift velocity $v_d$. The magnitude of drift velocity per unit electric field, $\mu = v_d/E$, is defined as the mobility of the charge carrier. Its SI unit is $m^2 V^{-1}s^{-1}$. Mobility is rela …

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10. CBSE 2020Set 55/3/11 markMCQ
    Q.$\mathrm{m^2\,V^{-1}\,s^{-1}}$ is the SI unit of which of the following ? (A) Drift velocity (B) Mobility (C) Resistivity (D) Potential gradient

    ›Reveal solutionSolution

    The unit $\mathrm{m^2\,V^{-1}\,s^{-1}}$ describes how much velocity a charge carrier gains per unit electric field — that's the definition of mobility. The answer is (B).

    When a charge carrier moves through a conductor under an electric field, two quantities matter: how fast it drifts (drift velocity) and how responsive it is to the field (mobility). The unit $\mathrm{m^2\,V^{-1}\,s^{-1}}$ tells us we're measuring a velocity-per-field ratio, which is precisely what mobility captures.

    Let's check each option systematically by dimensional analysis.

    1. Drift velocity is simply a speed — the average velocity of charge carriers in a conductor when an electric field is applied. Its SI unit is $\mathrm{m\,s^{-1}}$, not $\mathrm{m^2\,V^{-1}\,s^{-1}}$. So (A) is out.

    2. Mobility $\mu$ is defined as the drift velocity $v_d$ acquired per unit electric field $E$:

    $\mu = \frac{v_d}{E}$

    The electric field $E$ has units $\mathrm{V\,m^{-1}}$ (voltage per distance). Therefore:

    $[\mu] = \frac{\mathrm{m\,s^{-1}}}{\mathrm{V\,m^{-1}}} = \frac{\mathrm{m\,s^{-1}} \cdot \mathrm{m}}{\mathrm{V}} = \mathrm{m^2\,V^{-1}\,s^{-1}}$

    This matches exactly. …

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11. CBSE 2019Set 55/1/11 mark
    Q.How does the mobility of electrons in a conductor change, if the potential difference applied across the conductor is doubled, keeping the length and temperature of the conductor constant?

    ›Reveal solutionSolution

    Mobility of electrons in a conductor is independent of the applied potential difference — it depends only on the material and temperature. Doubling the voltage does not change mobility.

    The Concept: What Mobility Really Means

    Mobility ($\mu$) is a material property that tells us how fast an electron can drift through a conductor when an electric field is applied. It is defined as:

    $\mu = \frac{v_d}{E}$

    where $v_d$ is the drift velocity of electrons and $E$ is the electric field inside the conductor.

    The key insight: mobility is not a measure of how many electrons move, but how easily they move through the lattice. It depends on:

    • The nature of the material (atomic structure, number of free electrons)
    • Temperature (which affects lattice vibrations and scattering)

    It does not depend on the applied voltage or current — those are external conditions.

    Step-by-Step Reasoning

    1. What happens when voltage is doubled?

       For a conductor of fixed length $L$, the electric field is $E = V/L$. Doubling $V$ doubles $E$.

    2. How does drift velocity respond?

       Drift velocity is proportional to the electric field: $v_d \propto E$. So when $E$ doubles, $v_d$ also doubles. This is because a stronger field exerts a larger force on each electron ($F = eE$), accelerating it more between collisions.

    3. Now look at the mobility formula:

       $\mu = v_d / E$. If both $v_d$ and $E$ double, their ratio stays exactly the same.

       Mathematically:

    $\mu_{\text{new}} = \frac{2v_d}{2E} = \frac{v_d}{E} = \mu_{\text{old}}$

    4. The deeper reason — why mobility is constant here: Mobility is determined by the average time between collisions ($\tau$) of electrons with lattice ions:

    $\mu = \frac{e\tau}{m}$

    where $e$ is electron charge and $m$ is electron mass. …

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12. CBSE 2019Set ANNUAL1 mark
    Q.Write the unit of mobility.

    ›Reveal solutionSolution

    Mobility is drift velocity per unit electric field, so its unit is (m/s) divided by (V/m), giving m²V⁻¹s⁻¹.

    Mobility $\mu$ of a charge carrier is defined as the magnitude of drift velocity acquired per unit applied electric field:

    $\mu = \dfrac{v_d}{E}$

    Units: $v_d$ is in $\text{m s}^{-1}$, and $E$ (electric field) is in $\text{V m}^{-1}$. So: …

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