In electromagnetic theory, the electric and magnetic phenomena are related to each other. Therefore, the dimensions of electric and magnetic quantities must also be related to each other. In the questions below, $[E]$ and $[B]$ stand for dimensions of electric and magnetic fields respectively, while $\left[\varepsilon_0\right]$ and $\left[\mu_0\right]$ stand for dimensions of the permittivity and permeability of free space respectively. $[L]$ and $[T]$ are dimensions of length and time respectively. All the quantities are given in $SI$ units.

($1$) The relation between $[E]$ and $[B]$ is

$(A)$ $[ E ]=[ B ][ L ][ T ]$  $(B)$ $[ E ]=[ B ][ L ]^{-1}[ T ]$  $(C)$ $[ E ]=[ B ][ L ][ T ]^{-1}$  $(D)$ $[ E ]=[ B ][ L ]^{-1}[ T ]^{-1}$

($2$) The relation between $\left[\varepsilon_0\right]$ and $\left[\mu_0\right]$ is

$(A)$ $\left[\mu_0\right]=\left[\varepsilon_0\right][ L ]^2[ T ]^{-2}$  $(B)$ $\left[\mu_0\right]=\left[\varepsilon_0\right][ L ]^{-2}[ T ]^2$   $(C)$ $\left[\mu_0\right]=\left[\varepsilon_0\right]^{-1}[ L ]^2[ T ]^{-2}$  $(D)$ $\left[\mu_0\right]=\left[\varepsilon_0\right]^{-1}[ L ]^{-2}[ T ]^2$

Give the answer or quetion ($1$) and ($2$)

  • [IIT 2018]
  • A

    $C,D$

  • B

    $C,A$

  • C

    $C,B$

  • D

    $B,C,D$

Similar Questions

Match List $I$ with List $II$
List $I$ List $II$
$A$ Torque  $I$ ${\left[\mathrm{M}^1 \mathrm{~L}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-2}\right]}$
$B$ Magnetic fileld  $II$ $\left[\mathrm{L}^2 \mathrm{~A}^1\right]$
$C$ Magnetic moment $III$ ${\left[\mathrm{M}^1 \mathrm{~T}^{-2} \mathrm{~A}^{-1}\right]}$
$D$ Permeability of free  space $IV$ $\left[\mathrm{M}^1 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]$
Choose the correct answer from the options given below :

  • [JEE MAIN 2024]

The equation of a circle is given by $x^2+y^2=a^2$, where $a$ is the radius. If the equation is modified to change the origin other than $(0,0)$, then find out the correct dimensions of $A$ and $B$ in a new equation: $(x-A t)^2+\left(y-\frac{t}{B}\right)^2=a^2$.The dimensions of $t$ is given as $\left[ T ^{-1}\right]$.

  • [JEE MAIN 2023]

Write principle of Homogeneity of dimension.

Which of the following relation cannot be deduced using dimensional analysis? [the symbols have their usual meanings]

If velocity $v$, acceleration $A$ and force $F$ are chosen as fundamental quantities, then the dimensional formula of angular momentum in terms of $v,\,A$ and $F$ would be