(B) The magnetic field $B$ at the center of a circular current loop is given by $B = \frac{\mu_{0} I}{2r}$.Here, the current $I$ is due to the revolvi

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$\frac{\mu_{0} eL}{4 \pi m r^{3}}$

(B) The magnetic field $B$ at the center of a circular current loop is given by $B = \frac{\mu_{0} I}{2r}$.Here, the current $I$ is due to the revolving electron: $I = \frac{e}{T} = \frac{e}{2 \pi r / v} = \frac{ev}{2 \pi r}$.Substituting $I$ into the magnetic field formula: $B = \frac{\mu_{0}}{2r} \left( \frac{ev}{2 \pi r} \right) = \frac{\mu_{0} ev}{4 \pi r^{2}}$.The angular momentum $L$ of the electron is $L = mvr$, which implies $v = \frac{L}{mr}$.Substituting $v$ into the expression for $B$: $B = \frac{\mu_{0} e}{4 \pi r^{2}} \left( \frac{L}{mr} \right) = \frac{\mu_{0} eL}{4 \pi m r^{3}}$.

Class 12 Physics Moving Charges and Magnetism Biot-Savart's Law and its application

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An electron of mass $m$ is revolving around the nucleus in a circular orbit of radius $r$ and has angular momentum $L$. The magnetic field produced by the electron at the centre of the orbit is ($e = \text{electric charge}$, $\mu_{0} = \text{permeability of free space}$)

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A
$\frac{\mu_{0} eL}{4 \pi m r^{2}}$
B
$\frac{\mu_{0} eL}{4 \pi m r^{3}}$
C
$\frac{\mu_{0} eL}{2 \pi m r^{2}}$
D
$\frac{\mu_{0} eL}{2 \pi m r^{3}}$

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Moving Charges and Magnetism

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Biot-Savart's Law and its application

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Two circular loops $L_1$ and $L_2$ of wire carrying equal and opposite currents are placed parallel to each other with a common axis. The radius of loop $L_1$ is $R_1$ and that of $L_2$ is $R_2$. The distance between the centres of the loops is $\sqrt{3} R_1$. The magnetic field at the centre of $L_2$ shall be zero if

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An electron of mass $m$ is revolving around the nucleus in a circular orbit of radius $r$ and has angular momentum $L$. The magnetic field produced by the electron at the centre of the orbit is ($e = \text{electric charge}$, $\mu_{0} = \text{permeability of free space}$)

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The magnetic field at a perpendicular distance of $1 \,m$ from a long straight wire carrying a current of $1 \,A$ is:

$A$ particle having a charge $100 e$ is revolving in a circular path of radius $0.8 \ m$ with $1 \ r.p.s$. The magnetic field produced at the center of the circle in $SI$ unit is ($\mu_0$ is the permeability of vacuum,$e = 1.6 \times 10^{-19} \ C$).

$PQRS$ is a square loop made of uniform conducting wire. If the current enters the loop at $P$ and leaves at $S$, then the magnetic field will be

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