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Asked in GUJCET 2020 · Dimensional formula of a named quantity
Given: the polarization P of a dielectric.
Idea: P is the electric dipole moment induced per unit volume, P=p/(volume) with p=qd.
[q]=[It]=T¹A¹, so [p]=L¹T¹A¹.
Dividing by a volume: [P]=(L¹T¹A¹)/(L³)=L⁻²A¹T¹.
So the polarization has the dimensions L⁻²A¹T¹ -- the same as a surface charge density, C m⁻², which is what the bound charge on the faces of the slab is.
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