Question

Match List-I with List-II 
\[\begin{array}{|l|l|} \hline \text{List-I (Physical Quantity)} & \text{List-II (Units)} \\ \hline \text{(A) Magnetic field} & \text{(I) J T\(^{-1}\)} \\ \hline \text{(B) Magnetic moment} & \text{(II) T m A\(^{-1}\)} \\ \hline \text{(C) Pole strength} & \text{(III) J T\(^{-1}\) m\(^{-1}\)} \\ \hline \text{(D) Permeability of free space} & \text{(IV) Wb m\(^{-2}\)} \\ \hline \end{array}\]Choose the correct answer from the options given below: 
 

• (A) - (IV), (B) - (II), (C) - (III), (D) - (I)
• (A) - (IV), (B) - (I), (C) - (III), (D) - (II)
• (A) - (II), (B) - (I), (C) - (IV), (D) - (III)
• (A) - (IV), (B) - (III), (C) - (I), (D) - (II)

Hint:

For matching questions involving units, try to recall a defining formula for each physical quantity. For example, for magnetic field, \(B = F/(qv)\) or \(B = \Phi/A\). For magnetic moment, \(U = -MB\). These fundamental relationships are the key to deriving the units if you don't remember them directly.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This question requires matching physical quantities related to magnetism with their corresponding SI units. This involves recalling the definitions and key formulas for each quantity to derive or identify their units.

Step 2: Detailed Explanation:
Let's analyze each physical quantity and find its unit.
(A) Magnetic field (B):
The magnetic field is also known as magnetic flux density. The unit of magnetic flux is the Weber (Wb) and the unit of area is m². Therefore, Magnetic Field \(B = \frac{\text{Magnetic Flux}}{\text{Area}}\). Its unit is Wb/m² or Wb m\(^{-2}\). The unit Wb/m² is also called the Tesla (T). So, (A) matches with (IV).
(B) Magnetic moment (M):
The potential energy \(U\) of a magnetic dipole in a magnetic field \(B\) is given by \(U = -M B \cos\theta\). From this, the magnitude of the magnetic moment can be expressed as \(M = U/B\). The unit of energy \(U\) is Joule (J) and the unit of magnetic field \(B\) is Tesla (T). So, the unit of magnetic moment is J/T or J T\(^{-1}\). So, (B) matches with (I).
(C) Pole strength (m):
The magnetic moment \(M\) is defined as the product of pole strength \(m\) and magnetic length \(l\), i.e., \(M = m \times l\). Therefore, pole strength \(m = M/l\). Using the unit for M from the previous step (J T\(^{-1}\)) and the unit for length \(l\) (m), we get the unit for pole strength as (J T\(^{-1}\)) / m or J T\(^{-1}\) m\(^{-1}\). So, (C) matches with (III).
(D) Permeability of free space (\(\mu_0\)):
From the Biot-Savart law or Ampere's law, we can find the units. For a long solenoid, the magnetic field inside is \(B = \mu_0 n I\), where \(n\) is the number of turns per unit length (unit: m\(^{-1}\)) and \(I\) is the current (unit: A). So, \(\mu_0 = \frac{B}{nI}\). The unit for \(\mu_0\) would be \(\frac{\text{T}}{\text{m}^{-1} \cdot \text{A}} = \text{T m A}^{-1}\). So, (D) matches with (II).

Step 3: Final Answer:
Based on the analysis: (A) \(\rightarrow\) (IV) (B) \(\rightarrow\) (I) (C) \(\rightarrow\) (III) (D) \(\rightarrow\) (II) This corresponds to option (B).