Question

Match List-I with List-II (Symbols have their usual meanings).

Choose the correct answer from the options given below:

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

Hint:

Remember the four important formulas: \[ B=\frac{\mu_0 I}{2\pi r},\qquad B=\frac{\mu_0 I}{2r},\qquad F=BIl\sin\theta,\qquad \tau=BIA\sin\theta \] These are frequently asked in matching-type questions.

Answer 1

The Correct Option is D

Concept: Standard expressions from Moving Charges and Magnetism: \[ B_{\text{straight wire}} = \frac{\mu_0 I}{2\pi r} \] \[ B_{\text{circular coil}} = \frac{\mu_0 I}{2r} \] \[ F = BIl\sin\theta \] \[ \tau = BIA\sin\theta \]

Step 1: Match each quantity with its formula. For an infinitely long straight conductor, \[ B=\frac{\mu_0 I}{2\pi r} \] Hence, \[ (A)\rightarrow(III) \] For a circular coil at its centre, \[ B=\frac{\mu_0 I}{2r} \] Hence, \[ (B)\rightarrow(IV) \] Force on a current carrying conductor is \[ F=BIl\sin\theta \] Hence, \[ (C)\rightarrow(I) \] Torque on a current loop is \[ \tau=BIA\sin\theta \] Hence, \[ (D)\rightarrow(II) \]

Step 2: Write the final matching. \[ (A)\rightarrow(III),\quad (B)\rightarrow(IV),\quad (C)\rightarrow(I),\quad (D)\rightarrow(II) \] \[ \boxed{ \begin{array}{c} (A)-(III),\ (B)-(IV), (C)-(I),\ (D)-(II) \end{array} } \]