Import Question JSON

Current Question (ID: 20508)

Question:

$\text{A cube with side length } 25 \text{ cm is moving with a uniform velocity of } 8 \text{ m/s in the positive } y\text{-direction, as shown in the figure.}$ $\text{The cube is placed in a uniform magnetic field of } 1 \text{ T, which is directed along the negative } z\text{-axis.}$ $\text{The magnitude of the induced EMF across the opposite faces of the cube is:}$

Options:

1. $2 \text{ V}$
2. $4 \text{ V}$
3. $8 \text{ V}$
4. $6 \text{ V}$

Solution:

$\text{Hint: } E = Bvl$ $\text{Step: Find the magnitude of the induced EMF across the opposite face of the cube.}$ $\text{The induced EMF across the opposite face of the cube is given by:}$ $E = B_{\perp} v l_{\perp}$ $\text{The length is perpendicular to the magnetic field and the velocity vector is shown in the figure below;}$ $E = 1 \times 8 \times 0.25 = 2 \text{ V}$ $\text{Hence, option (1) is the correct answer.}$

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
}