In each of the following questions, Match column-I and column-II and select the correct match out of the four given choices.\begin{tabular}{l|l} Column - I & Column - II \end{tabular} (A) Biot-savart's law (P) Direction of magnetic field induction (B) Right hand thumb rule (Q) Magnitude of magnetic field induction (C) Fleming's left hand rule (R) Direction of induced current (D) Fleming's right hand rule (S) Direction of force due to a mag. field (a) $\mathrm{A} \rightarrow \mathrm{Q} ; \mathrm{B} \rightarrow \mathrm{P} ; \mathrm{C} \rightarrow \mathrm{R} ; \mathrm{D} \rightarrow \mathrm{S}$ (b) $\mathrm{A} \rightarrow \mathrm{Q} ; \mathrm{B} \rightarrow \mathrm{P} ; \mathrm{C} \rightarrow \mathrm{S} ; \mathrm{D} \rightarrow \mathrm{R}$ (c) $\mathrm{A} \rightarrow \mathrm{P} ; \mathrm{B} \rightarrow \mathrm{Q} ; \mathrm{C} \rightarrow \mathrm{R} ; \mathrm{D} \rightarrow \mathrm{S}$ (d) $\mathrm{A} \rightarrow \mathrm{P}: \mathrm{B} \rightarrow \mathrm{Q}: \mathrm{C} \rightarrow \mathrm{S} ; \mathrm{D} \rightarrow \mathrm{R}$

Step by step solution

01

Identifying the principles and their properties

(A) Biot-Savart's Law is used to find the magnetic field induced by a current-carrying conductor. It is mainly used for the magnitude and direction of the magnetic field. → The correct match for this is Magnitude of magnetic field induction (Q). (B) The Right Hand Thumb Rule (also known as the Right-Hand Grip Rule) is used to find the direction of the magnetic field due to a current-carrying conductor (wire). → The correct match for this is Direction of magnetic field induction (P). (C) Fleming's Left Hand Rule is used to find the direction of force experienced by a current-carrying wire in a magnetic field. → Correct match is Direction of force due to a magnetic field (S). (D) Fleming's Right Hand Rule is used to determine the direction of induced current in a conductor moving in a magnetic field. → Correct match is Direction of induced current (R).

02

Selecting the correct match from the given options

Now, we will compare the connections we have made in Step 1 with the given options: (a) A → Q; B → P; C → R; D → S (b) A → Q; B → P; C → S; D → R (c) A → P; B → Q; C → R; D → S (d) A → P; B → Q; C → S; D → R We found the connections to be A → Q; B → P; C → S; D → R which matches with the option (b). Hence, the correct answer is (b) \(\mathrm{A} \rightarrow \mathrm{Q} ; \mathrm{B} \rightarrow \mathrm{P} ; \mathrm{C} \rightarrow \mathrm{S} ; \mathrm{D} \rightarrow \mathrm{R}\).

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