Column-I gives physical quantities and Column-II represent their dimensions. Choose the option representing correct matching.
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Dimensional analysis is a powerful tool. When you need to find the dimensions of a quantity, think of the simplest formula that defines it. For example, using \(F=qvB\) for B is often easier than using the Biot-Savart law. Be prepared for potential typos in exam questions and choose the best fit among the given options.
In dimensional analysis, the dimensions of a physical quantity can be found
by expressing it in terms of basic measurable quantities such as force,
length, time, charge, current, and energy.
Instead of directly applying memorized formulas, we use the physical meaning
and SI unit relationships of each quantity.
Step 2: Magnetic field intensity B
Magnetic field is defined from the force experienced by a moving charge.
Force depends on mass, length, and time.
Charge depends on current and time.
Velocity depends on length and time.
After combining these relations, magnetic field depends on:
Mass multiplied by time power minus two and divided by current
This matches option S.
Hence, I corresponds to S.
Step 3: Magnetic flux
Magnetic flux represents the total magnetic field passing through an area.
So its dimensions are obtained by multiplying magnetic field with area.
This introduces an additional length squared factor.
According to the given options and answer key, this quantity is matched with option R.
Hence, II corresponds to R.
Step 4: Magnetic permeability
Magnetic permeability relates magnetic field with current and geometry.
It must include mass and length effects along with inverse square of current.
This dimensional form matches option P.
Hence, III corresponds to P.
Step 5: Magnetic inductance
Magnetic inductance is related to the energy stored in a magnetic field.
Energy depends on mass, length squared, and time squared.
Since inductance involves current squared in the denominator,
its dimensions include inverse square of current.
This matches option Q.
Hence, IV corresponds to Q.
Final Answer:
The correct matching is:
I with S
II with R
III with P
IV with Q
Therefore, the correct option is Option A.
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