Import Question JSON

Current Question (ID: 16769)

Question:

$\text{Two straight horizontal parallel wires carry the same current in the same direction, and } d \text{ is the distance between them. You are given a small magnetic needle that is freely suspended. Which of the following positions will have the needle's orientation independent of the magnitude of the current in the wires?}$

Options:

1. $\text{At a distance } \frac{d}{2} \text{ from any of the wires in any plane.}$
2. $\text{At a distance } \frac{d}{3} \text{ from any of the wires in the horizontal plane.}$
3. $\text{Anywhere on the circumference of a vertical circle of radius } d \text{ and centre halfway between the wires.}$
4. $\text{At points halfway between the wires in the horizontal plane.}$

Solution:

$\text{At a point between the wires at a distance } \frac{d}{2} \text{ from any of the wires, the orientation of the needle be independent of the magnitude of current in the wires; since the Lorentz force acting due to the two wires will be equal and in opposite direction.}$ $\text{At these points, the resultant field } = 0$

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
}