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AIIMS 2011
Exam
AIIMS
Year
2011
Subject
Physics
Chapter
Units and Dimensions

AIIMS 2011 · Physics · Units and Dimensions

What is the dimensions of magnetic field B in terms of C (=...

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

Options

  1. A[M1 L1 T−2C]\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{C}\right]
  2. B[M1 L0 T−1C−1]\left[\mathrm{M}^1 \mathrm{~L}^0 \mathrm{~T}^{-1} \mathrm{C}^{-1}\right]
  3. C[M1 L0 T−2C]\left[\mathrm{M}^1 \mathrm{~L}^0 \mathrm{~T}^{-2} \mathrm{C}\right]
  4. D[M1 L0 T−1C]\left[\mathrm{M}^1 \mathrm{~L}^0 \mathrm{~T}^{-1} \mathrm{C}\right]

Correct answer

B. [M1 L0 T−1C−1]\left[\mathrm{M}^1 \mathrm{~L}^0 \mathrm{~T}^{-1} \mathrm{C}^{-1}\right]

Step-by-step 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}
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