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What are the dimensions of magnetic induction in the SI system?
Step 1
Magnetic induction, also known as magnetic flux density or magnetic field density, is denoted by the symbol \( \mathbf{B} \). It represents the magnitude and direction of the magnetic field at a point in space. Show more…
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In the formula, $a=3 b c^{2} ' a^{\prime}$ and $' c^{\prime}$ have dimensions of electric capacitance and magnetic induction respectively. What are dimensions of ' $b^{\prime}$ in MKS system : (a) $\left[\mathrm{M}^{-3} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{Q}^{4}\right]$ (b) $\left[\mathrm{M}^{-3} \mathrm{~T}^{4} \mathrm{Q}^{4}\right]$ (c) $\left[\mathrm{M}^{-3} \mathrm{~T}^{3} \mathrm{Q}\right]$ (d) $\left[\mathrm{M}^{-3} \mathrm{~L}^{2} \mathrm{~T}^{4} \mathrm{Q}^{-4}\right]$
In the formula, $a=3 b c^{2}, a$ and $c$ have dimensions of electric capacitance and magnetic induction respectively. What are dimensions of $b$ in MKS system? (a) $\left[\mathrm{M}^{-3} \mathrm{~L}^{-2} \mathrm{~T}^{4} \mathrm{Q}^{4}\right]$ (b) $\left[\mathrm{M}^{-3} \mathrm{~T}^{4} \mathrm{Q}^{4}\right]$ (c) $\left[\mathrm{M}^{-3} \mathrm{~T}^{3} \mathrm{Q}\right]$ (d) $\left[\mathrm{M}^{-3} \mathrm{~L}^{2} \mathrm{~T}^{4} \mathrm{Q}^{-4}\right]$
Units and Measurements
Round 1
In the formula $X=3 Y Z^{2}, X$ and $Z$ have the dimensions of capacitance and magnetic induction, respectively. The dimensions of $Y$ in M.K.S. system are a. $M^{-3} L^{-2} T^{-2} A^{-4}$ b. $M L^{-2} \dot{A}$ c. $M^{-3} L^{-2} T^{8} A^{4}$ d. $M^{-3} L^{-2} T^{4} A^{4}$
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