Import Question JSON

Current Question (ID: 16518)

Question:

$\text{The electric field intensity and the electric potential at a point are } E \text{ and } V \text{ respectively. Which of the following is correct?}$

Options:

1. $\text{If } E \neq 0, V \text{ cannot be zero}$
2. $\text{If } V \neq 0, E \text{ cannot be zero}$
3. $\text{If } V \text{ is constant and non-zero, } E \text{ must be zero}$
4. $\text{If } V = 0, E \text{ must be zero}$

Solution:

$\text{Hint: The electric field is } E = -\frac{dV}{dx}$ $\text{Step 1: Consider two equal and opposite point charges}$ $V_C = \frac{kq}{r} - \frac{kq}{r} = 0$ $E_C = \frac{2kq}{r^2}$ $\text{Step 2: Consider a hollow conductor.}$ $\text{Hollow conductor}$ $E = 0$ $V \neq 0$

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
}