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: Concept Grasp:
This query requires associating physical quantities within magnetism with their respective SI units. It necessitates recalling definitions and fundamental formulas for each quantity to determine or identify their units.

Step 2: Detailed Analysis:
Let's examine each physical quantity to determine its unit.
(A) Magnetic Field (B):
The magnetic field is also termed magnetic flux density. The unit for magnetic flux is the Weber (Wb), and the unit for 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 known as the Tesla (T). Thus, (A) corresponds to (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). Therefore, the unit of magnetic moment is J/T or J T\(^{-1}\). Thus, (B) corresponds to (I).
(C) Pole Strength (m):
The magnetic moment \(M\) is defined as the product of pole strength \(m\) and magnetic length \(l\), i.e., \(M = m \times l\). Consequently, pole strength \(m = M/l\). Using the unit for M from the preceding step (J T\(^{-1}\)) and the unit for length \(l\) (m), we obtain the unit for pole strength as (J T\(^{-1}\)) / m or J T\(^{-1}\) m\(^{-1}\). Thus, (C) corresponds to (III).
(D) Permeability of Free Space (\(\mu_0\)):
Units can be derived from the Biot-Savart law or Ampere's law. 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). Thus, \(\mu_0 = \frac{B}{nI}\). The unit for \(\mu_0\) would be \(\frac{\text{T}}{\text{m}^{-1} \cdot \text{A}} = \text{T m A}^{-1}\). Thus, (D) corresponds to (II).

Step 3: Final Determination:
Based on the analysis:(A) \(\rightarrow\) (IV)(B) \(\rightarrow\) (I)(C) \(\rightarrow\) (III)(D) \(\rightarrow\) (II)This aligns with option (B).