
The dimensional formula for magnetic induction is:
A.
B.
C.
D.
Answer
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Hint: We know one of the equation for magnetic induction is . We know that the dimensional formula of magnetic moment is and the dimensional formula for magnetic susceptibility is and finally the dimensional formula for distance is .
Complete answer:
So, the dimensional formula of magnetic induction
Dimensional formula – Every physical quantity has a unit assigned for it, for example, the force has a unit . 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 .
Here represents mass, represents the length, represents time, and represents current.
We know that the equation for the magnetic induction is
Here, Magnetic induction
The magnetic moment or the magnetic dipole moment of the magnetic dipole
The magnetic permeability of free space
The distance of the point from the axis of the dipole
We know that the dimensional formula of magnetic moment is and the dimensional formula for magnetic susceptibility is and finally the dimensional formula for distance is .
So, the dimensional formula of magnetic induction
The dimensional formula of magnetic induction
The dimensional formula of magnetic induction
Therefore, the dimension formula for magnetic induction is
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.
Complete answer:
So, the dimensional formula of magnetic induction
Dimensional formula – Every physical quantity has a unit assigned for it, for example, the force has a unit
Here
We know that the equation for the magnetic induction is
Here,
We know that the dimensional formula of magnetic moment is
So, the dimensional formula of magnetic induction
The dimensional formula of magnetic induction
The dimensional formula of magnetic induction
Therefore, the dimension formula for magnetic induction is
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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