A planet with earth like magnetic field can be considered as a bar magnet. Suppose, we have such a bar magnet. We will treat it amagnetic dipole. Its dipole moment is given by the i = Hyj+ µ;k which remains unchanged without the application of externalmagnetic field. Suppose, a uniform magnetic field given by, B = ((53.0) j + (52.0) k) × 10° Tesla. Some neutron stars can generatesuch intense magnetic field. When this magnetic field is applied, the bar magnet starts to rotate. At some instant during rotation, consider(31.000730299786028) × 1028.0i N m and potential energy isit as "position 1" of the dipole, it's torque is 7 =-4516.319182112894 × 1029.0 J.Ua) Find the y and z component of magnetic dipole moment at this position?b) What is the angle between magnetic dipole moment and magnetic field in this position?c) Calculate the minimum potential energy the dipole moment can have in the applied magnetic field.d) Find the y and z component of magnetic dipole moment at the minimum potential energy position?e) How much energy is lost by the bar magnet when it comes to minimum potential energy position from position 1?f) What is the magnitude of magnetic dipole moment before it starts to rotate and at position 1?g) How much external energy is required to keep the dipole in maximum potential energy position?IS

Given,μ→=μy j^+μz k^B→=53j^+52k^×109 Tτ→=31×1029 i^ NmU=-4516.319 ×1029J

A planet with earth like magnetic field can be considered as a bar magnet. Suppose, we have such a bar magnet. We will treat it a magnetic dipole. Its dipole moment is given by the i = µyj + µ,k which remains unchanged without the application of external magnetic field. Suppose, a uniform magnetic field given by, B = ((53.0) j + (52.0) k) × 10° Tesla. Some neutron stars can generate such intense magnetic field. When this magnetic field is applied, the bar magnet starts to rotate. At some instant during rotation, consider it as "position 1" of the dipole, it's torque is 7 = U = -4516.319182112894 × 1029.0 J. (31.000730299786028) × 1029.0% N - m and potential energy is a) Find the y and z component of magnetic dipole moment at this position? b) What is the angle between magnetic dipole moment and magnetic field in this position? c) Calculate the minimum potential energy the dipole moment can have in the applied magnetic field. d) Find the y and z component of magnetic dipole moment at the minimum potential energy position? e) How much energy is lost by the bar magnet when it comes to minimum potential energy position from position 1? f) What is the magnitude of magnetic dipole moment before it starts to rotate and at position 1? g) How much external energy is required to keep the dipole in maximum potential energy position?

A planet with earth like magnetic field can be considered as a bar magnet. Suppose, we have such a bar magnet. We will treat it a magnetic dipole. Its dipole moment is given by the i = µyj + µ,k which remains unchanged without the application of external magnetic field. Suppose, a uniform magnetic field given by, B = ((53.0) j + (52.0) k) × 10° Tesla. Some neutron stars can generate such intense magnetic field. When this magnetic field is applied, the bar magnet starts to rotate. At some instant during rotation, consider it as "position 1" of the dipole, it's torque is 7 = U = -4516.319182112894 × 1029.0 J. (31.000730299786028) × 1029.0% N - m and potential energy is a) Find the y and z component of magnetic dipole moment at this position? b) What is the angle between magnetic dipole moment and magnetic field in this position? c) Calculate the minimum potential energy the dipole moment can have in the applied magnetic field. d) Find the y and z component of magnetic dipole moment at the minimum potential energy position? e) How much energy is lost by the bar magnet when it comes to minimum potential energy position from position 1? f) What is the magnitude of magnetic dipole moment before it starts to rotate and at position 1? g) How much external energy is required to keep the dipole in maximum potential energy position?

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