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Current Question (ID: 16516)

Question:

$\text{In a certain region of space with volume } 0.2 \text{ m}^3, \text{ the electric potential is found to be } 5 \text{ V throughout. The magnitude of the electric field in this region is:}$

Options:

1. $0.5 \text{ N/C}$
2. $1 \text{ N/C}$
3. $5 \text{ N/C}$
4. $\text{zero}$

Solution:

$\text{Hint: } |\vec{E}| = \left| -\frac{dV}{dx} \right|$ $\text{Step: Calculate } \vec{E} \text{ for the given potential.}$ $\text{As the potential is uniform everywhere i.e., } 5 \text{ V as shown in the figure.}$ $\Rightarrow \vec{E} = -\frac{dV}{dx}$ $\text{The variation of potential with respect to position is zero i.e., } \frac{dV}{dx} = 0$ $\Rightarrow |\vec{E}| = 0$ $\text{Therefore, the magnitude of the electric field in the given region is zero.}$ $\text{Hence, option (4) is the correct answer.}$

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
}