Question

Match List I with List II 

List I (Current configuration)		List II(Magnetic field at point O)
A		i	\(B_0=\frac{\mu_0I}{4\pi r}[\pi+2]\)
B		ii	\(B_0=\frac{\mu_0}{4}\frac{I}{r}\)
C		iii	\(B_0=\frac{\mu_0I}{2\pi r}[\pi-1]\)
D		iv	\(B_0=\frac{\mu_0I}{4\pi r}[\pi+1]\)

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

Answer 1

The Correct Option is C

1. Configuration A: - Using Biot-Savart's law, the magnetic field at point \(O\) is: \[ B = \frac{\mu_0 I}{4\pi r} [\pi + 2]. \]
2. Configuration B: - The magnetic field at \(O\) is: \[ B = \frac{\mu_0 I}{4\pi r} [2\pi - 1]. \]
3. Configuration C: - The magnetic field at \(O\) is: \[ B = \frac{\mu_0 I}{4\pi r} [\pi - 1]. \]
4. Configuration D: - The magnetic field at \(O\) is: \[ B = \frac{\mu_0 I}{4\pi r} [2\pi + 1]. \]
Thus, the correct match is: A-III, B-I, C-IV, D-II. The magnetic field at a point due to a current configuration is calculated using Biot-Savart's law or Ampère's circuital law.