Question

The relation between $E$ and $B$ is

• A. $\begin{array}{l}\left[E\right]=\left[B\right]\left[L\right]\left[T\right]\end{array}$
• B. $\begin{array}{l}\left[E\right]=\left[B\right]{\left[L\right]}^{-1}\left[T\right]\end{array}$
• C. $\begin{array}{l}\left[E\right]=\left[B\right]\left[L\right]{\left[T\right]}^{-1}\end{array}$
• D. $\begin{array}{l}\left[E\right]=\left[B\right]{\left[L\right]}^{-1}{\left[T\right]}^{-1}\end{array}$

Answer 1

The correct option is C

$\begin{array}{l}\left[E\right]=\left[B\right]\left[L\right]{\left[T\right]}^{-1}\end{array}$

Explanation for Correct Option:

Option (C):

Let the electric field be $E$, magnetic field be $B$ and speed of light be $c$.

We know that,

$$\begin{gathered} B=\frac{E}{c} \\ \Rightarrow E=Bc \end{gathered}$$

We know that the unit of speed it $m{s}^{-1}$.

This can be dimensionally written as $\left[L\right]{\left[T\right]}^{-1}$.

Let us write this dimensionally to get,

$\left[E\right]=\left[B\right]\left[L\right]{\left[T\right]}^{-1}$

Hence, the correct answer is option (C).