(C) The magnetic moment $m$ of a solenoid is given by $m = N i A$,where $N$ is the number of turns,$i$ is the current,and $A$ is the cross-sectional a

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(C) The magnetic moment $m$ of a solenoid is given by $m = N i A$,where $N$ is the number of turns,$i$ is the current,and $A$ is the cross-sectional area.Magnetization $\vec M$ is defined as the magnetic moment per unit volume $V$.$V = A \ell$,where $\ell$ is the length of the solenoid.Therefore,$|\vec M| = \frac{m}{V} = \frac{N i A}{A \ell} = \frac{N i}{\ell}$.Given $N = 500$,$i = 15\,A$,and $\ell = 25\,cm = 0.25\,m$.$|\vec M| = \frac{500 \times 15}{0.25} = \frac{7500}{0.25} = 30000\,A m^{-1}$.

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

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$A$ $25\,cm$ long solenoid has radius $2\,cm$ and $500$ total number of turns. It carries a current of $15\,A.$ If it is equivalent to a magnet of the same size and magnetization $\vec M$ (magnetic moment per unit volume),then $\left| {\vec M} \right|$ is

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A
$30000\pi \,A m^{-1}$
B
$3\pi \,A m^{-1}$
C
$30000 \,A m^{-1}$
D
$300 \,A m^{-1}$

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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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$A$ long solenoid is formed by winding $70$ turns $cm^{-1}$. If $2.0\,A$ current flows,then the magnetic field produced inside the solenoid is $.......\times 10^{-4}\,T$ $\left(\mu_0 = 4\pi \times 10^{-7}\,TmA^{-1}\right)$

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$A$ $25\,cm$ long solenoid has radius $2\,cm$ and $500$ total number of turns. It carries a current of $15\,A.$ If it is equivalent to a magnet of the same size and magnetization $\vec M$ (magnetic moment per unit volume),then $\left| {\vec M} \right|$ is

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$A$ long solenoid is formed by winding $70$ turns $cm^{-1}$. If $2.0\,A$ current flows,then the magnetic field produced inside the solenoid is $.......\times 10^{-4}\,T$ $\left(\mu_0 = 4\pi \times 10^{-7}\,TmA^{-1}\right)$

$A$ toroid has a core (non-ferromagnetic) of inner radius $24 \ cm$ and outer radius $26 \ cm$ around which $2000$ turns of a wire are wound. If the current in the wire is $12 \ A$, the magnetic field inside the core of the toroid is:

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Assertion: The magnetic field produced by a current-carrying solenoid is independent of its length and cross-sectional area.
Reason: The magnetic field inside the solenoid is uniform.