Calculate the polarisation vector of the material which has 100 dipoles per unit volume in a volume of 2 units.

The polarization vector, ( mathbf{P} ), of a material is defined as the dipole moment per unit volume. So, if we have 100 dipoles per unit volume, and each dipole has a dipole moment ( mathbf{p} ) (which you haven’t specified), and the total volume considered is 2 units, we can proceed with the calculation given proper values.

If each dipole has a dipole moment ( mathbf{p} ), the total dipole moment ( mathbf{P}_{text{total}} ) for 100 dipoles is:

[ mathbf{P}_{text{total}} = 100 times mathbf{p} ]

However, to calculate the polarization vector ( mathbf{P} ), we need the dipole moment per unit volume. Since we are considering a total volume of 2 units and we have 100 dipoles per unit volume, the overall number of dipoles in this volume is:

[ text{Number of dipoles in 2 units of volume} = 100 times 2 = 200 ]

So, the total dipole moment in this volume is:

[ mathbf{P}_{text{total}} = 200 times mathbf{p} ]

The polarization vector ( mathbf{P} ) is then:

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