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The dimensional formula of self inductance is ________.

Asked in GUJCET 2023 · Units and dimensions

• (1) M¹L¹T⁻²A⁻²
• (2) M¹L²T⁻²A⁻²
• (3) M⁻¹L⁻¹T²A²
• (4) M¹L⁻¹T⁻¹A⁻²

Step-by-step solution

Why the other options are wrong

• (1) M¹L¹T⁻²A⁻² is the dimensional formula of μ₀, one power of length short of the answer. It comes from stopping at μ₀ in L=μ₀n²ℓ A: the n² contributes L⁻² and ℓ A contributes L³, so together they add one more length.
• (3) M⁻¹L⁻¹T²A² is the reciprocal of μ₀, which is not the reciprocal of anything asked for here; every exponent differs from the answer. Sanity check: L=Φ/I with [Φ]=M¹L²T⁻²A⁻¹ fixes it at M¹L²T⁻²A⁻².
• (4) M¹L⁻¹T⁻¹A⁻² has both the length and the time exponents wrong. Sanity check by the energy route: U=1/2LI² gives [L]=(M¹L²T⁻²)/(A²)=M¹L²T⁻²A⁻².

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