Question

Dimensional formula for electric field is _________

• A. $\left[M{L}^2{T}^{-3}{A}^{-1}\right]$
• B. $\left[M{L}^2{T}^{-3}{A}^{-2}\right]$
• C. $\left[ML{T}^{-3}{A}^{-1}\right]$
• D. $\left[M^0{L}^0{T}^0{A}^0\right]$

Answer 1

Answer: (C)

$\left[ML{T}^{-3}{A}^{-1}\right]$

$\text{Step 1: Identifying simplest formula for Electric field}$

We know that,

$E=\frac{F}{q}$ $....\left(1\right)$

Where, $F$ is force and $q$ is charge.

$\text{Step 2: Calculationg Dimensions}$

We know that, Force $F=m\times a=\left[M\right]\times \left[L{T}^{-2}\right]$.

Where $m$ is mass and$a$ is acceleration,

And, Charge $q=It=\left[A\right]\times \left[T\right]$

Where $I$ is current and $t$ is time

So, Dimensions of Electric field, using equation $\left(1\right)$

$\left[E\right]=\frac{\left[F\right]}{\left[q\right]}=\frac{\left[M\right]\left[L\right]\left[T^{-2}\right]}{\left[A\right]\left[T\right]}$ $=\left[ML{T}^{-3}{A}^{-1}\right]$

Hence, correct Option is $C$