Magnetic Effects Of Current And Magnetism

• Step 1: The total number of unpaired electrons is 6, which means that there are 6 electrons contributing to the magnetic moment.
• Step 2: According to Hund’s rules, the total angular momentum is determined by the maximum multiplicity, which means we have the highest total spin.
• Step 3: The formula for the effective magnetic moment is given by: where is the number of unpaired electrons.
• Step 4: For 6 unpaired electrons, . So, we can calculate the effective magnetic moment as:
• Step 5: The value rounds to 0 Bohr magnetons in some cases or approximations where this is considered negligible.

Step 1: The magnetic field outside a uniformly magnetized cylinder cannot generally be expressed as the gradient of a scalar function. This is because the magnetization generates a non-conservative magnetic field in the region outside the cylinder, which contradicts the option (A).
Step 2: The bound volume current density is related to the magnetization by: Since the magnetization is uniform, its curl is zero, and thus, the bound volume current density is zero, making option (B) correct.
Step 3: The surface current density on the curved surface of the cylinder is given by: Since the magnetization is uniform and along the axis of the cylinder, there is a non-zero surface current density on the curved surface, which makes option (C) correct.
Step 4: On the flat surfaces (top and bottom), the magnetization does not produce a current, as the magnetization is parallel to the cylinder's axis. Therefore, the surface current densities on the flat surfaces are zero, making option (D) incorrect.

• Step 1: The total number of unpaired electrons is 6, which means that there are 6 electrons contributing to the magnetic moment.
• Step 2: According to Hund’s rules, the total angular momentum is determined by the maximum multiplicity, which means we have the highest total spin.
• Step 3: The formula for the effective magnetic moment is given by: where is the number of unpaired electrons.
• Step 4: For 6 unpaired electrons, . So, we can calculate the effective magnetic moment as:
• Step 5: The value rounds to 0 Bohr magnetons in some cases or approximations where this is considered negligible.