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The dimensional formula for magnetic induction is:
A. MT1A1
B. MT2A1
C. MLA1
D. MT2A

Answer
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Hint: We know one of the equation for magnetic induction is B=μ04π×2mr3 . We know that the dimensional formula of magnetic moment is [M0L2T0A1] and the dimensional formula for magnetic susceptibility is [M1L1T2A2] and finally the dimensional formula for distance is (r)=[M0L1T0A0] .

Complete answer:
So, the dimensional formula of magnetic induction =[M1T2A1]

Dimensional formula – Every physical quantity has a unit assigned for it, for example, the force has a unit kgm/s2. When we express this unit in terms of the fundamental quantities we get the dimensional formula of that physical quantity. The dimensional formula for force is [MLT2A0] .
Here M represents mass, L represents the length, T represents time, and A represents current.

We know that the equation for the magnetic induction is
B=μ04π×2mr3
Here, B= Magnetic induction
m= The magnetic moment or the magnetic dipole moment of the magnetic dipole
u0= The magnetic permeability of free space
r= The distance of the point from the axis of the dipole
We know that the dimensional formula of magnetic moment is [M0L2T0A1] and the dimensional formula for magnetic susceptibility is [M1L1T2A2] and finally the dimensional formula for distance is (r)=[M0L1T0A0] .
So, the dimensional formula of magnetic induction =[M1L1T2A2]×[M0L2T0A1][M0L1T0A0]
The dimensional formula of magnetic induction =[M1L0T2A1]
The dimensional formula of magnetic induction =[M1T2A1]

Therefore, the dimension formula for magnetic induction is [M1T2A1]

So, the correct answer is “Option B”.

Note:
Dimensional formula is unique, whereas the unit can be measured in the SI unit system, metric system, etc. So, for example, the unit for magnetic induction is Tesla in the SI unit but weber per square meter is also a unit of magnetic induction.
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