Question

Which physical quantity has the unit $ Wb{m^{ - 2}} $ ? Is it a scalar or vector quantity?

Answer 1

Hint: In order to solve this question, we should know that those physical quantities which have only magnitude but no direction are called scalar quantities whereas those physical quantities which have magnitude as well as direction are known as vector quantities. Here, we will first discuss a given unit of weber and square meter inverse and then we will figure out a formula which represents this relation and then check whether it’s a scalar or vector quantity.

Complete Step By Step Answer:
In magnetism physics, the magnetic flux is defined as the product of magnetic field and area to which these magnetic field lines pass and it is mathematically written as $ \phi = B.A $ where $ \phi $ represent magnetic flux, B represent magnetic field and A represent area. and the SI unit to represent magnetic flux is called Weber which is written as Wb. and the SI unit of magnetic field which is a vector quantity is called Tesla denoted by T and for area the SI unit is $ {m^2}. $
so we can write the units relation as $ Wb = T{m^2} $ according to the relation $ \phi = B.A $ and from this relation, another relation is derived called magnetic flux density which is simply the magnetic flux per unit of area so, magnetic flux density can be written as $ \dfrac{\phi }{A} $ and from the relation $ \phi = B.A $ we can say, $ \dfrac{\phi }{A} = B $ so, here B represent the magnetic flux density which has the units of $ \dfrac{{Wb}}{{{m^2}}} = Wb{m^{ - 2}} $ Hence, it’s the magnetic flux density denoted by ‘B’ which has the units of $ Wb{m^{ - 2}} $ . and B is the magnetic field lines which has its own direction so ‘B’ magnetic flux density is a vector quantity.

Note:
It should be remembered that, magnetic flux density is nothing but simply the representation of number of magnetic field lines passing per unit area and the SI unit of magnetic field is known as Tesla so, the units $ Wb{m^{ - 2}} $ can also be called simply Tesla.