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Current Question (ID: 20182)

Question:

$\text{The electric potential at any point } (x, y, z) \text{ m in space is given by } V = 3x^2 \text{ V.}$ $\text{The electric field at the point } (1, 0, 3) \text{ m will be:}$

Options:

1. $3 \text{ V/m, directed along the positive } x\text{-axis}$
2. $3 \text{ V/m, directed along the negative } x\text{-axis}$
3. $6 \text{ V/m, directed along the positive } x\text{-axis}$
4. $6 \text{ V/m, directed along the negative } x\text{-axis}$

Solution:

$\text{Hint: } E = -\frac{dV}{dx}$ $\text{Step: Find the electric field.}$ $\vec{E} = -\frac{dV}{dx} \hat{i}$ $\Rightarrow \vec{E} = -6x \hat{i}$ $\text{Substitute } x = 1$ $\Rightarrow \vec{E} = -6 \hat{i} \text{ V/m}$ $\text{The negative sign indicates the field is along the negative } x\text{-axis.}$ $\text{Hence, option (4) is the correct answer.}$

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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
}