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Asked in GUJCET 2018 · Dimensional formula of a named quantity
Given: the mobility μ of a charge carrier.
Idea: mobility is the drift speed acquired per unit applied electric field, μ=(v_d)/E.
[v_d]=L¹T⁻¹ and [E]=M¹L¹T⁻³A⁻¹.
[μ]=(L¹T⁻¹)/(M¹L¹T⁻³A⁻¹)=M⁻¹L⁰T²A¹.
The lengths cancel, which is why mobility carries L⁰ even though its SI unit m² V⁻¹ s⁻¹ looks as if it should not.
So the dimensional formula of mobility is M⁻¹L⁰T²A¹.
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