If the potential is central, it must be spherically symmetric.GAGS said:While studying nuclear forces one question was raised that why electric quadrupole moment is zero while the potential is considerd central and spherically symmetric.
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A zero quadrupole moment refers to the absence of any net electric quadrupole moment in a system. This means that the distribution of electric charge within the system is symmetric and does not produce any dipole or quadrupole moment.
Zero quadrupole moment is important in physics because it can provide insights into the symmetry and properties of a system. It is also a necessary condition for certain physical phenomena, such as the conservation of angular momentum.
Any system that has a symmetric distribution of electric charge can have a zero quadrupole moment. This includes spherical, cylindrical, and planar distributions of charge.
A system with a zero quadrupole moment will not produce any electric field at large distances. This is because the electric field is directly proportional to the quadrupole moment of a system. Therefore, a system with a zero quadrupole moment will have a more uniform and isotropic electric field.
Yes, it is possible for a system to have a zero quadrupole moment but a non-zero dipole moment. This can occur when the positive and negative charges within the system are not perfectly aligned, resulting in a net dipole moment but a cancellation of the quadrupole moment.