(B) The magnetic energy density $(u_B)$ stored in a magnetic field $B$ is given by the formula: $u_B = \frac{B^2}{2\mu_0}$.We know that the speed of l

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$\frac{\varepsilon_0 c^2 B^2}{2}$

(B) The magnetic energy density $(u_B)$ stored in a magnetic field $B$ is given by the formula: $u_B = \frac{B^2}{2\mu_0}$.We know that the speed of light in vacuum is $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$,which implies $c^2 = \frac{1}{\mu_0 \varepsilon_0}$.From this,we can express the permeability of free space as $\mu_0 = \frac{1}{\varepsilon_0 c^2}$.Substituting this value of $\mu_0$ into the energy density formula:$u_B = \frac{B^2}{2(1 / \varepsilon_0 c^2)}$$u_B = \frac{\varepsilon_0 c^2 B^2}{2}$.Therefore,the correct option is $B$.

Class 12 Physics Moving Charges and Magnetism Ampere’s circuital law and its application (Solenoid and Toroid)

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If the magnetic field inside a solenoid is $B$,then the magnetic energy stored in it per unit volume is (where $c$ is the speed of light in vacuum and $\varepsilon_0$ is the permittivity of free space).

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A
$\varepsilon_0 c^2 B^2$
B
$\frac{\varepsilon_0 c^2 B^2}{2}$
C
$2 \varepsilon_0 c^2 B^2$
D
$\frac{\varepsilon_0 c^2 B^2}{4}$

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Class 12

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Moving Charges and Magnetism

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Ampere’s circuital law and its application (Solenoid and Toroid)

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$A$ thick uniformly charged hollow cylinder of inner radius $a$ and outer radius $b$ rotates with constant angular speed $\omega$ about its axis $APB$,with charge density $\rho$. Given that $L \gg a$ and $L \gg b$,and $P$ is the midpoint of $AB$. Choose the incorrect option.

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For a long current-carrying solenoid,the magnetic field inside is $0.6 \ T$. The magnetic energy per unit volume is . . . . . . .

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The correct curve between the magnetic induction $B$ along the axis of a long solenoid due to current flow $i$ in it and distance $x$ from one end is:

Medium

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Statement-$1$: Ampere's law can be used to find the magnetic field due to a finite length of a straight current-carrying wire.
Statement-$2$: The magnetic field due to a finite length of a straight current-carrying wire is symmetric about the wire.

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In a toroid,the magnetic field on the axis is to be calculated given the radius $r = 0.5 \, cm$,current $I = 1.5 \, A$,number of turns $N = 250$,and relative permeability $\mu_r = 700$. Find the magnetic field $B$ (in Tesla). (in $.5$)

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If the magnetic field inside a solenoid is $B$,then the magnetic energy stored in it per unit volume is (where $c$ is the speed of light in vacuum and $\varepsilon_0$ is the permittivity of free space).

Similar Questions

$A$ thick uniformly charged hollow cylinder of inner radius $a$ and outer radius $b$ rotates with constant angular speed $\omega$ about its axis $APB$,with charge density $\rho$. Given that $L \gg a$ and $L \gg b$,and $P$ is the midpoint of $AB$. Choose the incorrect option.

For a long current-carrying solenoid,the magnetic field inside is $0.6 \ T$. The magnetic energy per unit volume is . . . . . . .

The correct curve between the magnetic induction $B$ along the axis of a long solenoid due to current flow $i$ in it and distance $x$ from one end is:

Statement-$1$: Ampere's law can be used to find the magnetic field due to a finite length of a straight current-carrying wire.Statement-$2$: The magnetic field due to a finite length of a straight current-carrying wire is symmetric about the wire.

In a toroid,the magnetic field on the axis is to be calculated given the radius $r = 0.5 \, cm$,current $I = 1.5 \, A$,number of turns $N = 250$,and relative permeability $\mu_r = 700$. Find the magnetic field $B$ (in Tesla). (in $.5$)

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Statement-$1$: Ampere's law can be used to find the magnetic field due to a finite length of a straight current-carrying wire.
Statement-$2$: The magnetic field due to a finite length of a straight current-carrying wire is symmetric about the wire.