The dimensional formula for the physical quantityis $\frac{{{E^2}{\mu _0}{\varepsilon _0}}}{{{B^2}}}$ ($E =$ electric field and $B =$ magnetic field)
Medium
Download our app for free and get started
We know,
$\mu_0 \varepsilon_0=\frac{1}{ c ^2}$
$\frac{E}{B}=c$
$\frac{ E ^2 \mu_0 \varepsilon_0}{ B ^2}=1$
Dimension of $1=\left[ M ^0 L ^0 T ^0\right]$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A circular coil having $200$ turns, $2.5 \times 10^{-4} \mathrm{~m}^2$ area and carrying $100 \mu \mathrm{A}$ current is placed in a uniform magnetic field of $1 \mathrm{~T}$. Initially the magnetic dipole moment $(\vec{M})$ was directed along $\vec{B}$. Amount of work, required to rotate the coil through $90^{\circ}$ from its initial orientation such that $\overrightarrow{\mathrm{M}}$ becomes perpendicular to $\vec{B}$, is. . . . $\mu \mathrm{J}$.View Solution
- 2In the circuit, shown the galvanometer $G$ of resistance $60\, \Omega$ is shunted by a resistance $r=0.02\, \Omega$. The current through $R$ (in $ohm$) is nearly $1\, A$. The value of resistance $R$ (in $ohm$) is nearly (in $\Omega$)View Solution
- 3A charged particle is moving in a uniform magnetic field in a circular path. Radius of circular path is $R$. When energy of particle is doubled, then new radius will beView Solution
- 4The magnetic field at the centre of a circular coil of radius $r$ is $\pi $ times that due to a long straight wire at a distance $r$ from it, for equal currents. Figure here shows three cases : in all cases the circular part has radius $r$ and straight ones are infinitely long. For same current the $B$ field at the centre $P$ in cases $1$, $2$, $ 3$ have the ratioView Solution
- 5A current $i$ is flowing in a straight conductor of length $L.$ The magnetic induction at a point on its axis at a distance $\frac {L}{4}$ from its centre will beView Solution
- 6A charge $q$ $coulomb$ moves in a circle at $n$ revolutions per second and the radius of the circle is $r$ $metre$. Then magnetic field at the centre of the circle isView Solution
- 7A milliammeter of range $10\, mA$ has a coil of resistance $1 \,\Omega$. To use it as voltmeter of range $10\, volt$, the resistance that must be connected in series with it, will be ............. $\Omega $View Solution
- 8A uniform magnetic field $B$ of $0.3\, T$ is along the positive $Z-$ direction . A rectangular loop $(abcd)$ of sides $10\, cm\times5\, cm$ carries a current $I$ of $12\, A$. Out of the following different orientations which one corresponds to stable equilibrium ?View Solution
- 9The magnetic field $B$ with in the solenoid having $n$ $turns$ per $metre$ length and carrying a current of $i$ $ampere$ is given byView Solution
- 10A solenoid is $1.0$ $ metre$ long and it has $4250$ $turns$. If a current of $5.0$ $ampere$ is flowing through it, what is the magnetic field at its centre $[{\mu _0} = 4\pi \times {10^{ - 7}}\,weber/amp - m]$View Solution