Question

The electric field in a certain region is given by $\overrightarrow{E}=\left(\frac{K}{x^3}\right)\hat{i}$. the dimension of K are:-

• A. $ML{T}^{-3}{A}^{-1}$
• B. $M{L}^{-2}{T}^{-3}{A}^{-1}$
• C. $M{L}^4{T}^{-3}{A}^{-1}$
• D. $M^0{L}^0{T}^0{A}^0$

Answer 1

Answer: (C)

$M{L}^4{T}^{-3}{A}^{-1}$

The electric field in the given region is $\overrightarrow{E}=\frac{K}{x^3}\hat{i}$

The dimension for the electric field is $\left[M^1{L}^1{T}^{-3}{A}^{-1}\right]$

In order to obtain the dimension of $K$, simplify the above expression:

$K=E\cdot x^3$

Here $X$ denotes the position. So, dimensions of $x$ are $\left[L\right]$.

Simplify the above expression.

$K=\left[M^1{L}^1{T}^{-3}{A}^{-1}\right][L{]}^3$

$⟹\left[M^1{L}^4{T}^{-3}{A}^{-1}\right]$

Option $C$ is correct.