Question

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

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

Answer 1

The correct option is B $\left[M^1{L}^0{T}^{-1}{C}^{-1}\right]$

We know that force on a particle moving perpendicular to magnetic field is
$F=qvB$

$\Rightarrow B=\frac{F}{qv}$

Dimension of $F$ is $\left[M^1{L}^1{T}^{-2}\right]$

Dimension of $q$ is $\left[C^1\right]$

Dimension of $v$ is $\left[L^1{T}^{-1}\right]$

Hence, the dimensions of $B$ is $\left[M^1{L}^0{T}^{-1}{C}^{-1}\right]$