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Current Question (ID: 20366)

Question:

$\text{Two parallel infinite wires carry equal currents as shown. If both the currents are doubled and separation is halved, the force on a 10 cm section of one of the wires becomes:}$

Options:

1. $4 \text{ times}$
2. $\frac{1}{4} \text{ times}$
3. $8 \text{ times}$
4. $\frac{1}{8} \text{ times}$

Solution:

$\text{Hint: } F = \frac{\mu_0 I_1 I_2 l}{2 \pi d}$ $\text{Step: Find the force on a 10 cm section of one of the wires.}$ $\text{The magnetic force on the length } l \text{ of either wire is given by:}$ $F = \frac{\mu_0 I_1 I_2 l}{2 \pi d}$ $\text{The original force between the wires is given by:}$ $F = \frac{\mu_0 I_2^2 l}{2 \pi d} \quad \cdots (1)$ $\text{The new force between the wires is given by:}$ $F' = \frac{\mu_0 \times 4 I_2^2 l}{2 \pi \left( \frac{d}{2} \right)} = \frac{8 \mu_0 I_2^2 l}{2 \pi d} \quad \cdots (2)$ $\text{From the equation (1) and (2) we get;}$ $F' = 8F$ $\text{Hence, option (3) is the correct answer.}$

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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
}