Import Question JSON

Current Question (ID: 20423)

Question:

$\text{Two parallel, long wires are kept } 0.20 \text{ m apart in a vacuum, each carrying current of } x \text{ A in the same direction.}$ $\text{If the force of attraction per meter of each wire is } 2 \times 10^{-6} \text{ N, then the value of } x \text{ is approximately:}$ $1. \ 1$ $2. \ 2.4$ $3. \ 1.4$ $4. \ 2$

Options:

1. $1$
2. $2.4$
3. $1.4$
4. $2$

Solution:

$\text{Hint: The force per unit length is;} \frac{F}{l} = \frac{\mu_0 I_1 I_2}{2 \pi d}$ $\text{Step: Find the current passing through the wires.}$ $\text{The force per unit length is given by;} \Rightarrow \frac{F}{l} = \frac{\mu_0 I_1 I_2}{2 \pi d}$ $\text{Substitute the known values we get;} \Rightarrow 2 \times 10^{-6} = \frac{4 \pi \times 10^{-7} \times x^2}{2 \pi \times 0.2}$ $\Rightarrow x^2 = 0.2 \times 10$ $\Rightarrow x = \sqrt{2} \text{ A} = 1.414 \text{ A}$ $\text{Hence, option (3) is the correct answer.}$

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
}