Import Question JSON

Current Question (ID: 16963)

Question:

$\text{The adjoining figure shows two different arrangements in which two square}$ $\text{wireframes are placed in a uniform magnetic field } B \text{ decreasing with time.}$ $\text{The direction of the induced current } I \text{ in the figure is:}$

Options:

1. $\text{From } a \text{ to } b \text{ and from } c \text{ to } d$
2. $\text{From } a \text{ to } b \text{ and from } f \text{ to } e$
3. $\text{From } b \text{ to } a \text{ and from } d \text{ to } c$
4. $\text{From } b \text{ to } a \text{ and from } e \text{ to } f$

Solution:

$\text{Hint: The induced current flows from } b \text{ to } a \text{ and from } d \text{ to } c \text{ to oppose the}$ $\text{decreasing magnetic flux, following Lenz's Law.}$ $\text{Explanation:}$ $\text{Given: The magnetic field } B \text{ is decreasing with time. According to Lenz's}$ $\text{Law, the induced current will oppose this decrease, generating a magnetic}$ $\text{field in the same direction as the external field.}$ $\text{Loop I: To oppose the decrease in magnetic flux, the induced current will}$ $\text{create a magnetic field in the same direction as the external } B\text{-field.}$ $\text{Applying the right-hand rule:}$ $\text{The induced current in Loop I will flow from } b \text{ to } a \text{ to generate a field pointing}$ $\text{upwards.}$ $\text{Loop II: For the smaller loop, the induced current must create a field in the}$ $\text{same direction as the external } B\text{-field to oppose the decrease. Using the}$ $\text{right-hand rule, the induced current will flow from } d \text{ to } c \text{ to produce this field.}$ $\text{Therefore, the correct options is from } b \text{ to } a \text{ and from } d \text{ to } c.$ $\text{Hence, option (3) is the correct answer.}$

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
}