Question
Question: The dimensional formula of magnetic flux is: \( (a){\text{ }}\left[ {{M^1}{L^2}{T^{ - 1}}{A^{ - 2}...
The dimensional formula of magnetic flux is:
(a){\text{ }}\left[ {{M^1}{L^2}{T^{ - 1}}{A^{ - 2}}} \right] \\\
(b){\text{ }}\left[ {{M^1}{L^2}{T^{ - 2}}{A^{ - 1}}} \right] \\\
(c){\text{ }}\left[ {{M^1}{L^2}{T^{ - 1}}{A^{ - 1}}} \right] \\\
(d){\text{ }}\left[ {{M^1}{L^0}{T^{ - 2}}{A^{ - 1}}} \right] \\\
Solution
In this question use the relationship between magnetic flux density and the perpendicular area and magnetic flux that isϕ=B.A. Use the dimensional formula of the independent quantities in the relation and this will help out in taking out the dimensional formula for magnetic flux.
Complete answer:
As we all know magnetic flux is the multiplication of the magnetic flux density and the perpendicular area.
⇒ϕ=B.A
Where,
ϕ = magnetic flux often measured in i.e. S.I unit is weber.
B = magnetic flux density often measured in i.e. The S.I unit is Tesla.
A = area often measured in square meter.
Now the S.I unit of magnetic flux density is Tesla it is also denoted by weber per meter square or Newton amp meter
So B = AmN
And the unit of area = m2
So the unit of magnetic flux is ϕ=AmN×m2=ANm.................. (1)
Now as we know that Newton is also the unit of the force which is mass times acceleration.
I.e. F = ma,
Now as we know that the unit of kg so the dimension of Kg is [M]
And the unit of acceleration (a) is meter per Second Square.
Now as we know that the dimension of meter is [L] and the dimension of second is [T]
So the dimension of acceleration is [T2][L]
So the dimension of force or Newton is [MLT−2]
Now as we know that the unit of current is Ampere which has a standard dimension = [A]
Now from equation (1) the dimension of magnetic flux is,
ϕ=ANm=[A][MLT−2][L]=[M1L2T−2A−1]
So this is the required dimension of the magnetic flux.
Hence option (B) is the correct answer.
Note:
Dimension formula is the expression for the unit of a physical quantity in terms of the fundamental quantities. 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. The approach to find the dimensional formula remains the same in almost every problem however it is advised to remember some basic formula of magnetic flux while dealing with problems of this kind.