Import Question JSON

Current Question (ID: 16525)

Question:

$\text{Consider two points 1 and 2 in a region outside a charged sphere. Two points are not very far away from the sphere. If } \mathbf{E} \text{ and } V \text{ represent the electric field vector and the electric potential, which of the following is not possible?}$

Options:

1. $|\mathbf{E}_1| = |\mathbf{E}_2|, V_1 = V_2$
2. $\mathbf{E}_1 \neq \mathbf{E}_2, V_1 \neq V_2$
3. $\mathbf{E}_1 \neq \mathbf{E}_2, V_1 = V_2$
4. $|\mathbf{E}_1| = |\mathbf{E}_2|, V_1 \neq V_2$

Solution:

$\text{The electric field is a vector quantity but the electric potential is scalar.}$ $\text{For two different points at the same radial distance, the magnitude of the electric field can be the same but its direction will be different and the electric potential will also be the same.}$ $\text{Outside the charged sphere, (for equal distances from centre) if electric fields at two points are the same then both points must be equipotential points.}$

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
}