Import Question JSON

Current Question (ID: 20343)

Question:

$\text{Two very long, straight, and insulated wires are kept at } 90^\circ \text{ angle from each other in } xy\text{-plane as shown in the figure}$ $\text{These wires carry currents of equal magnitude } I, \text{ whose directions are shown in the figure. The net magnetic field at point } P \text{ will be:}$

Options:

1. $\text{zero}$
2. $-\frac{\mu_0 I}{2 \pi d} (\hat{x} + \hat{y})$
3. $\frac{\mu_0 I}{2 \pi d} (\hat{x} + \hat{y})$
4. $\frac{\mu_0 I}{\pi d} (\hat{z})$

Solution:

$\text{Hint: Magnetic field due to both wires are equal and opposite}$ $\vec{B} = \frac{\mu_0 I}{2 \pi d} \hat{k} - \frac{\mu_0 I}{2 \pi d} \hat{k}$ $\vec{B} = \hat{0}$

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
}