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Current Question (ID: 20342)

Question:

$\text{A circular coil with } N \text{ turns and radius } r \text{ carries a current } I. \text{ It is held in the } XZ\text{-plane within a magnetic field } \vec{B}. \text{ The torque on the coil due to the magnetic field is:}$

Options:

1. $\frac{B \pi r^2 I}{N}$
2. $\text{zero}$
3. $B \pi r^2 I N$
4. $\frac{B r^2 I}{\pi N}$

Solution:

$\text{Hint: } \vec{\tau} = \vec{M} \times \vec{B}$ $\text{Step: Find the value of torque on the coil due to the magnetic field.}$ $\text{The direction of the magnetic field and area element is shown in the figure below;}$ $\vec{A}$ $\vec{B}$ $\text{The torque acting on the coil is given by;}$ $\vec{\tau} = \vec{M} \times \vec{B}$ $\Rightarrow \tau = MB \sin \theta = MB \sin 90^\circ$ $\Rightarrow \tau = NI \pi r^2 B \quad [M = NIA]$ $\text{Hence, option (3) is the correct answer.}$

Import JSON File

Upload a JSON file containing LaTeX/MathJax formatted question, options, and solution.

Expected JSON Format:

{
  "question": "The mass of carbon present in 0.5 mole of $\\mathrm{K}_4[\\mathrm{Fe(CN)}_6]$ is:",
  "options": [
    {
      "id": 1,
      "text": "1.8 g"
    },
    {
      "id": 2,
      "text": "18 g"
    },
    {
      "id": 3,
      "text": "3.6 g"
    },
    {
      "id": 4,
      "text": "36 g"
    }
  ],
  "solution": "\\begin{align}\n&\\text{Hint: Mole concept}\\\\\n&1 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\text{ moles of carbon atom}\\\\\n&0.5 \\text{ mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6] = 6 \\times 0.5 \\text{ mol} = 3 \\text{ mol}\\\\\n&1 \\text{ mol of carbon} = 12 \\text{ g}\\\\\n&3 \\text{ mol carbon} = 12 \\times 3 = 36 \\text{ g}\\\\\n&\\text{Hence, 36 g mass of carbon present in 0.5 mole of } \\mathrm{K}_4[\\mathrm{Fe(CN)}_6].\n\\end{align}",
  "correct_answer": 4
}