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Unit of mobility in terms of fundamental units is ________.

Asked in GUJCET 2023 · Units and dimensions

• (1) kg⁻¹ s⁻² A
• (2) kg² A
• (3) kg⁻¹ s² A
• (4) kg⁻¹ s² A⁻¹

Step-by-step solution

Why the other options are wrong

• (1) kg⁻¹ s⁻² A has the sign of the second reversed. In μ=(v_d)/E the T⁻¹ of the speed is divided by the T⁻³ of the field, which leaves T⁺², so the seconds come out squared in the numerator.
• (2) kg² A would make the mobility grow as the square of a mass. The mass enters once only, through the field in the denominator, so the kilogram appears once and inverted -- and the seconds cannot vanish.
• (4) kg⁻¹ s² A⁻¹ inverts the ampere. The ampere reaches μ through the charge in E=F/q; being in the denominator of the field it ends up in the numerator of the mobility, as A⁺¹.

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