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Dimension of mobility (μ) is ________.

Asked in GSEB Board July 2021 · Dimensional formula of a named quantity

• (1) M¹L⁴T⁻⁴A⁻¹
• (2) M⁻¹L⁰T²A¹
• (3) M¹L³T⁻⁴A⁻¹
• (4) M¹L⁴T⁻³A⁻¹

Step-by-step solution

Why the other options are wrong

• (1) No single slip produces M¹L⁴T⁻⁴A⁻¹ -- it carries a positive mass and four powers of length, while mobility is a speed divided by a field, in which the lengths cancel exactly. Sanity check: μ=(v_d)/E fixes it at M⁻¹L⁰T²A¹.
• (3) M¹L³T⁻⁴A⁻¹ sits one current exponent away from Coulomb's constant, M¹L³T⁻⁴A⁻², and has nothing to do with the mobility. Sanity check: μ=(v_d)/E gives M⁻¹L⁰T²A¹ -- the lengths cancel and the mass comes out inverted.
• (4) M¹L⁴T⁻³A⁻¹ is [E]×L³, the field multiplied by a volume. It has the field the right way up, which is the mistake: the field belongs in the denominator of (v_d)/E.

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