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Current Question (ID: 20437)

Question:

$\text{A wire } X \text{ of length } 50 \text{ cm carrying a current } 2 \text{ A is placed parallel to a long wire } Y \text{ of length } 5 \text{ m.}$ $\text{The wire } Y \text{ carries a current } 3 \text{ A.}$ $\text{The distance between the two wires is } 5 \text{ cm and currents flow in the same direction.}$ $\text{The force acting on the wire } Y \text{ is:}$

Options:

1. $1.2 \times 10^{-5} \text{ N directed towards wire } X.$
2. $1.2 \times 10^{-4} \text{ N directed away from wire } X.$
3. $1.2 \times 10^{-4} \text{ N directed towards wire } X.$
4. $2.4 \times 10^{-5} \text{ N directed towards wire } X.$

Solution:

$\text{The force per unit length between two parallel currents is given by:}$ $F/L = \frac{\mu_0 I_1 I_2}{2\pi d}$ $\text{where } \mu_0 = 4\pi \times 10^{-7} \text{ Tm/A, } I_1 = 2 \text{ A, } I_2 = 3 \text{ A, } d = 0.05 \text{ m.}$ $F/L = \frac{4\pi \times 10^{-7} \times 2 \times 3}{2\pi \times 0.05}$ $= 2.4 \times 10^{-5} \text{ N/m}$ $\text{Total force on wire } Y = F/L \times L = 2.4 \times 10^{-5} \times 5 = 1.2 \times 10^{-4} \text{ N}$ $\text{The force is directed towards wire } X \text{ since the currents are in the same direction.}$

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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
}