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Select the dimensional formula of (B²)/(2μ₀).

Asked in GUJCET 2017 · Dimensional formula of a named quantity

• (1) M¹L¹T²
• (2) M⁻¹L¹T²
• (3) M⁻¹L⁻¹T⁻²
• (4) M¹L⁻¹T⁻²

Step-by-step solution

Why the other options are wrong

• (1) M¹L¹T² needs both mistakes at once: the ratio taken upside down and the mass left out of [B]. With [B] read as T⁻²A⁻¹, (2μ₀)/(B²)=(M¹L¹T⁻²A⁻²)/(T⁻⁴A⁻²)=M¹L¹T².
• (2) M⁻¹L¹T² is the reciprocal of the answer -- the expression turned over: (2μ₀)/(B²)=(M¹L¹T⁻²A⁻²)/(M²L⁰T⁻⁴A⁻²)=M⁻¹L¹T².
• (3) M⁻¹L⁻¹T⁻² comes from leaving the mass out of [B]: with [B] taken as T⁻²A⁻¹ instead of M¹T⁻²A⁻¹, (B²)/(μ₀)=(T⁻⁴A⁻²)/(M¹L¹T⁻²A⁻²)=M⁻¹L⁻¹T⁻².

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