Q103 / 180 · AIIMS 2011 · Physics

What is the dimensions of magnetic field $B$ in terms of $\mathrm{C}$ (= coulomb), M, L, T?

  • A
    $\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{C}\right]$
  • Correct answer
    B
    $\left[\mathrm{M}^1 \mathrm{~L}^0 \mathrm{~T}^{-1} \mathrm{C}^{-1}\right]$
  • C
    $\left[\mathrm{M}^1 \mathrm{~L}^0 \mathrm{~T}^{-2} \mathrm{C}\right]$
  • D
    $\left[\mathrm{M}^1 \mathrm{~L}^0 \mathrm{~T}^{-1} \mathrm{C}\right]$

Solution

$$ \begin{aligned} & \text { }: B=\frac{F}{q v}=\frac{\left[\mathrm{MLT}^{-2}\right]}{[\mathrm{AT}]\left[\mathrm{LT}^{-1}\right]}=\left[\mathrm{ML}^0 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right] \\ & \text { But }[A]=\left[C \mathrm{~T}^{-1}\right] \\ & \therefore \quad[B]=\left[\mathrm{ML}^0 \mathrm{~T}^{-1} \mathrm{C}^{-1}\right] \end{aligned} $$

Hence, the correct answer is option: 'B'.

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