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(A) The orbital magnetic moment $\vec{m}$ of an electron revolving in a circular orbit is given by $\vec{m} = I \vec{A}$,where $I$ is the current and

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$m$ and $L$ are in opposite directions perpendicular to the plane of the orbit.

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(A) The orbital magnetic moment $\vec{m}$ of an electron revolving in a circular orbit is given by $\vec{m} = I \vec{A}$,where $I$ is the current and $\vec{A}$ is the area vector. Since the electron is negatively charged,the direction of the equivalent current $I$ is opposite to the direction of the electron's motion. By the right-hand rule,the direction of $\vec{m}$ is perpendicular to the plane of the orbit.The angular momentum $\vec{L}$ of the electron is given by $\vec{L} = \vec{r} 	imes \vec{p}$,where $\vec{p} = m_e \vec{v}$ is the linear momentum. According to the right-hand rule for the cross product,the direction of $\vec{L}$ is also perpendicular to the plane of the orbit.Because the electron has a negative charge,the direction of the magnetic moment $\vec{m}$ is opposite to the direction of the angular momentum $\vec{L}$. Therefore,$\vec{m}$ and $\vec{L}$ are in opposite directions perpendicular to the plane of the orbit.

An electron is moving in an orbit around the nucleus in an atom. Let $m$ be the orbital magnetic moment and $L$ be the angular momentum of the electron,then

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