The dimension of $\frac{\mathrm{B}^{2}}{2 \mu_{0}}$, where $\mathrm{B}$ is magnetic field and $\mu_{0}$ is the magnetic permeability of vacuum, is
The dimension of $\frac{\mathrm{B}^{2}}{2 \mu_{0}}$, where $\mathrm{B}$ is magnetic field and $\mu_{0}$ is the magnetic permeability of vacuum, is
- [JEE MAIN 2020]
- A
$M L^{-1} T^{-2}$
- B
$\mathrm{ML}^{2} \mathrm{T}^{-1}$
- C
$\mathrm{ML} \mathrm{T}^{-2}$
- D
$\mathrm{ML}^{2} \mathrm{T}^{-2}$
Similar Questions
Obtain the relation between the units of some physical quantity in two different systems of units. Obtain the relation between the $MKS$ and $CGS$ unit of work.
A length-scale $(l)$ depends on the permittivity $(\varepsilon)$ of a dielectric material. Boltzmann constant $\left(k_B\right)$, the absolute temperature $(T)$, the number per unit volune $(n)$ of certain charged particles, and the charge $(q)$ carried by each of the particless. Which of the following expression($s$) for $l$ is(are) dimensionally correct?
($A$) $l=\sqrt{\left(\frac{n q^2}{\varepsilon k_B T}\right)}$
($B$) $l=\sqrt{\left(\frac{\varepsilon k_B T}{n q^2}\right)}$
($C$)$l=\sqrt{\left(\frac{q^2}{\varepsilon n^{2 / 3} k_B T}\right)}$
($D$) $l=\sqrt{\left(\frac{q^2}{\varepsilon n^{1 / 3} k_B T}\right)}$
A length-scale $(l)$ depends on the permittivity $(\varepsilon)$ of a dielectric material. Boltzmann constant $\left(k_B\right)$, the absolute temperature $(T)$, the number per unit volune $(n)$ of certain charged particles, and the charge $(q)$ carried by each of the particless. Which of the following expression($s$) for $l$ is(are) dimensionally correct?
($A$) $l=\sqrt{\left(\frac{n q^2}{\varepsilon k_B T}\right)}$
($B$) $l=\sqrt{\left(\frac{\varepsilon k_B T}{n q^2}\right)}$
($C$)$l=\sqrt{\left(\frac{q^2}{\varepsilon n^{2 / 3} k_B T}\right)}$
($D$) $l=\sqrt{\left(\frac{q^2}{\varepsilon n^{1 / 3} k_B T}\right)}$
- [IIT 2016]
A beaker contains a fluid of density $\rho \, kg / m^3$, specific heat $S\, J / kg\,^oC$ and viscosity $\eta $. The beaker is filled upto height $h$. To estimate the rate of heat transfer per unit area $(Q / A)$ by convection when beaker is put on a hot plate, a student proposes that it should depend on $\eta \,,\,\left( {\frac{{S\Delta \theta }}{h}} \right)$ and $\left( {\frac{1}{{\rho g}}} \right)$ when $\Delta \theta $ (in $^oC$) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for $(Q / A)$ is
- [JEE MAIN 2015]
A physical quantity $\vec{S}$ is defined as $\vec{S}=(\vec{E} \times \vec{B}) / \mu_0$, where $\vec{E}$ is electric field, $\vec{B}$ is magnetic field and $\mu_0$ is the permeability of free space. The dimensions of $\vec{S}$ are the same as the dimensions of which of the following quantity (ies)?
$(A)$ $\frac{\text { Energy }}{\text { charge } \times \text { current }}$
$(B)$ $\frac{\text { Force }}{\text { Length } \times \text { Time }}$
$(C)$ $\frac{\text { Energy }}{\text { Volume }}$
$(D)$ $\frac{\text { Power }}{\text { Area }}$
A physical quantity $\vec{S}$ is defined as $\vec{S}=(\vec{E} \times \vec{B}) / \mu_0$, where $\vec{E}$ is electric field, $\vec{B}$ is magnetic field and $\mu_0$ is the permeability of free space. The dimensions of $\vec{S}$ are the same as the dimensions of which of the following quantity (ies)?
$(A)$ $\frac{\text { Energy }}{\text { charge } \times \text { current }}$
$(B)$ $\frac{\text { Force }}{\text { Length } \times \text { Time }}$
$(C)$ $\frac{\text { Energy }}{\text { Volume }}$
$(D)$ $\frac{\text { Power }}{\text { Area }}$
- [IIT 2021]
if Energy is given by $U = \frac{{A\sqrt x }}{{{x^2} + B}},\,$, then dimensions of $AB$ is
if Energy is given by $U = \frac{{A\sqrt x }}{{{x^2} + B}},\,$, then dimensions of $AB$ is