Question

Find the dimensions of the electric dipole moment $p$. The defining equations are $p=q.d$ and $M=IA$; where $d$ is the distance, $A$ is area, $q$ is the charge and $I$ is current.

Answer 1

Hint: In this question think of the two charges that are equal and opposite and are distant by some distance. Then the basic formula for dipole along with the basics of current, that is the rate flow of charge, will help get the SI unit and the dimension of the electric dipole moment.

Complete step by step answer:
Electric dipole moment is used to measure the polarity of the system. Let us suppose that there are two charges which have equal magnitude, one is positively charged (+Q) and other is negatively charged (–Q), let these charges be separated by a distance (d).

So this combination is known as an electric dipole moment. Hence we can say that an electric dipole moment is the combination of equal and opposite charges separated by a distance as shown in the above figure.So as we see that the dipole moment has a charge which is measured in coulomb and separated by a distance which is measured in meters.

So the S.I unit of the dipole moment is coulomb-meter. As we know that the electrons flow from the negatively charged to the positively charged dipole moment has a specific direction.Therefore it is a vector quantity (i.e. both magnitude as well as direction).As we know that the current is the rate of change of charge w.r.t time.
\[ \Rightarrow I = \dfrac{{dQ}}{{dt}}\]
\[ \Rightarrow Q = It\]

Now as we know that the unit of current is amp and dimension of current is \[A\]. Now as we know, the unit of time is second and the dimension of second is \[T\]. So the dimension of charge is \[\left[ {AT} \right]\]. Now as we know that the unit of distance is meter so the dimension of distance is \[L\]. So the dimension of the dipole moment is \[\left[ {ATL} \right]\].

Hence the unit of dipole moment is coulomb-meter and the dimension is \[\left[ {ATL} \right]\] respectively.

Note: It should be remembered that the basics of dimension formula is very helpful for solving these kinds of problems. Dimensional formula is basically an expression depicting the units of physical quantity in terms of the fundamental quantities that are worldwide used for measurement. The fundamental quantities are mass (M), Length (L) and time (T). A dimensional formula is expressed in terms of power of M,L and T.