Import Question JSON

Current Question (ID: 16804)

Question:

$\text{If a long hollow copper pipe carries a direct current along its length, then the magnetic field associated with the current will be:}$

Options:

1. $\text{only inside the pipe}$
2. $\text{only outside the pipe}$
3. $\text{both inside and outside the pipe}$
4. $\text{zero everywhere}$

Solution:

$\text{Hint: Use Ampere's circuital law.}$ $\text{Explanation: According to Ampere's circuital law,}$ $B(2\pi r) = \mu_0 \times 0$ $\text{or}$ $B = 0$ $\text{So, inside a hollow metallic (copper) pipe carrying current, the magnetic field is zero.}$ $\text{But for external points, the whole current behaves as if it were concentrated at the axis only, so outside}$ $B_0 = \frac{\mu_0 i}{2\pi r}$ $\text{Then, the magnetic field is produced outside the pipe only.}$ $\text{For a loop inside the hollow portion of the conductor, the current enclosed is zero until the loop is on the surface or inside the material of the conductor.}$ $B_{\text{inside}} = 0$ $\text{For any loop outside, the current enclosed by the amperian loop is not zero, hence the magnetic field is non-zero.}$ $\text{Hence, option (2) is the correct answer.}$

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
}