Import Question JSON

Current Question (ID: 16415)

Question:

$\text{The figure shows the electric lines of force emerging from a charged body. If the electric field at } A \text{ and } B \text{ are } E_A \text{ and } E_B \text{ respectively and if the displacement between } A \text{ and } B \text{ is } r, \text{ then:}$

Options:

1. $E_A > E_B$
2. $E_A < E_B$
3. $E_A = \frac{E_B}{r}$
4. $E_A = \frac{E_B}{r^2}$

Solution:

$\text{Hint: } E \propto \frac{1}{r^2}$ $\text{Explanation: The electric field lines are closer at } A \text{ than at } B, \text{ indicating that the electric field at } A (E_A) \text{ is stronger than the field at } B (E_B).$ $\text{In a non-uniform electric field, the intensity is higher where the lines are denser.}$ $\text{The electric field strength is inversely proportional to the square of the distance from the source charge:}$ $E \propto \frac{1}{r^2}$ $\text{If } E_A \text{ and } E_B \text{ represent the field strengths at points } A \text{ and } B, \text{ we can write the relationship:}$ $\Rightarrow E_A = \frac{E_B}{r^2}$ $\text{Hence, option (1) is the correct answer.}$

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
}