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Current Question (ID: 20039)

Question:

$\text{Given below are two statements:}$ $\text{Statement I:}$ \text{An electric dipole is placed at the centre of a hollow sphere. The flux of the electric field through the sphere is zero but the electric field is not zero anywhere in the sphere.}$ $\text{Statement II:}$ \text{If } R \text{ is the radius of a solid metallic sphere and } Q \text{ be the total charge on it. The electric field at any point on the spherical surface of radius } r \ (< R) \text{ is zero but the electric flux passing through this closed spherical surface of radius } r \text{ is not zero.}$

Options:

1. $\text{Both Statement I and Statement II are true}$
2. $\text{Statement I is true but Statement II is false}$
3. $\text{Both Statement I and Statement II are false}$
4. $\text{Statement I is false but Statement II is true}$

Solution:

$\text{Hint: } \phi = \frac{q_{\text{enclosed}}}{\varepsilon_0}$ $\oint \vec{E} \cdot \vec{ds} = \frac{q_{\text{in}}}{\varepsilon_0} = 0 = \phi$ $\text{The flux of } \vec{E} \text{ through the sphere is zero. But } \oint \vec{E} \cdot \vec{ds} = 0$ $\Rightarrow \left\{ \vec{E} \cdot \vec{ds} \neq 0 \right\} \text{ for small section ds only}$ $\text{Statement - 2}$ $\phi = \oint \vec{E} \cdot \vec{ds} = 0$ $\text{As charge encloses within the Gaussian surface is equal to zero.}$ $\text{Option (2) statement-1 correct statement-2 false.}$

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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
}