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 \(B_0=\frac{\mu_0I}{4\pi r}[\pi+1]\)
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 | \(B_0=\frac{\mu_0I}{4\pi r}[\pi+1]\) |
Updated On: Jun 25, 2025
- A-III, B-IV, C-I, D-II
- A-I, B-III, C-IV, D-II
- A-III, B-I, C-IV, D-II
- A-II, B-I, C-IV, D-III
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The Correct Option is C
Solution and Explanation
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.
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.
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Concepts Used:
Magnetic Field
The magnetic field is a field created by moving electric charges. It is a force field that exerts a force on materials such as iron when they are placed in its vicinity. Magnetic fields do not require a medium to propagate; they can even propagate in a vacuum. Magnetic field also referred to as a vector field, describes the magnetic influence on moving electric charges, magnetic materials, and electric currents.
A magnetic field can be presented in two ways.
- Magnetic Field Vector: The magnetic field is described mathematically as a vector field. This vector field can be plotted directly as a set of many vectors drawn on a grid. Each vector points in the direction that a compass would point and has length dependent on the strength of the magnetic force.
- Magnetic Field Lines: An alternative way to represent the information contained within a vector field is with the use of field lines. Here we dispense with the grid pattern and connect the vectors with smooth lines.
Properties of Magnetic Field Lines
- Magnetic field lines never cross each other
- The density of the field lines indicates the strength of the field
- Magnetic field lines always make closed-loops
- Magnetic field lines always emerge or start from the north pole and terminate at the south pole.