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Current Question (ID: 16455)

Question:

$\text{Given below are two statements:}$ $\text{Assertion (A): A charge } q \text{ is placed in a cube of side } b. \text{ The flux associated}$ $\text{with the cube is independent of side length.}$ $\text{Reason (R): Gauss's law is independent of the size of the Gaussian}$ $\text{surface.}$

Options:

1. $\text{Both (A) and (R) are True and (R) is the correct explanation of (A).}$
2. $\text{Both (A) and (R) are True but (R) is not the correct explanation of (A).}$
3. $\text{(A) is True but (R) is False.}$
4. $\text{Both (A) and (R) are False.}$

Solution:

$\text{Hint: } \phi_E = \frac{q_{\text{enc}}}{\varepsilon_0}$ $\text{Explanation: Let's analyze the two statements one by one:}$ $\text{Assertion (A): "A charge } q \text{ is placed inside a cube of side } b. \text{ The flux}$ $\text{associated with the cube is independent of side length."}$ $\text{According to Gauss's Law, the electric flux through a closed surface depends}$ $\text{only on the net charge enclosed within the surface, not on the shape or size}$ $\text{of the surface.}$ $\text{Gauss’s law states:}$ $\phi_E = \frac{q_{\text{enc}}}{\varepsilon_0}$ $\text{Thus, the flux through the cube will only depend on the charge } q, \text{ not on the}$ $\text{side length } b. \text{ So, Assertion (A) is true.}$ $\text{Reason (R): "Gauss's law is independent of the size of the Gaussian}$ $\text{surface."}$ $\text{This statement is true because Gauss’s law only depends on the charge}$ $\text{enclosed by the surface, not the size or shape of the surface.}$ $\text{Both the Assertion (A) and the Reason (R) are true. The Reason (R) correctly}$ $\text{explains the Assertion (A) because the flux through the Gaussian surface is}$ $\text{independent of its size due to the nature of Gauss's law.}$ $\text{Hence, option (1) is the correct answer.}$

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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
}