Import Question JSON

Current Question (ID: 16418)

Question:

$\text{A thin conducting ring of the radius } R \text{ is given a charge } +Q. \text{ The electric field at the centre } O \text{ of the ring due to the charge on the part } AKB \text{ of the ring is } E. \text{ The electric field at the centre due to the charge on the part } ACDB \text{ of the ring is:}$

Options:

1. $3E \text{ along } KO$
2. $E \text{ along } OK$
3. $E \text{ along } KO$
4. $3E \text{ along } OK$

Solution:

$\text{Hint: } \vec{E} = 0$ $\text{Step: Find the electric field at the centre.}$ $\text{It is given that the ring is conducting, so the electric field at the centre will be zero.}$ $\vec{E}_{AKB} + \vec{E}_{ACDB} = 0$ $\vec{E}_{ACDB} = -\vec{E}_{AKB}$ $\vec{E}_{ACDB} = E \text{ (along } KO)$ $\text{Therefore, the electric field at the centre due to the charge on the part } ACDB \text{ of the ring is } E \text{ along } OK.$ $\text{Hence, option (2) is the correct answer.}$

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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
}