Import Question JSON

Current Question (ID: 16866)

Question:

$\text{Which one of the following is correct?}$

Options:

1. $\text{The magnetic field lines also represent the lines of force on a moving charged particle at every point.}$
2. $\text{The magnetic field lines can be entirely confined within the core of a toroid, but not within a straight solenoid.}$
3. $\text{A bar magnet exerts a torque on itself due to its own field.}$
4. $\text{The magnetic field arises due to stationary charges.}$

Solution:

$\text{Hint: Use the concept of magnetic field and magnetic force.}$ $\text{Explanation: Analyze each option one by one:}$ $\text{The magnetic field lines indicate the direction of the magnetic field, but the force on a moving charged particle is given by the Lorentz force } \vec{F} = q(\vec{v} \times \vec{B}).$ $\text{The force is perpendicular to both the velocity and the field, not along the field lines. This statement is incorrect.}$ $\text{In a toroid, the magnetic field lines form closed loops confined within the core. In a straight solenoid, while most field lines are confined, some fringing occurs at the ends, meaning not all lines remain confined. This statement is correct.}$ $\text{A magnet does not exert a torque on itself. Torque requires an external field interacting with the magnetic moment of the magnet. There is no force or torque on an element due to the field produced by that element itself. But there is a force (or torque) on an element of the same wire. (For the special case of a straight wire, this force is zero.) This statement is incorrect.}$ $\text{A magnetic field arises from moving charges or currents, not from stationary charges. Stationary charges produce only electric fields. This statement is incorrect.}$ $\text{Hence, option (2) is the correct answer.}$

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
}