Import Question JSON

Current Question (ID: 16795)

Question:

$\text{When a proton is released from rest in a room, it starts with an initial acceleration } a_0 \text{ towards the east.}$ $\text{When it is projected towards the north with a speed of } v_0, \text{ it moves with an initial acceleration of } 3a_0 \text{ towards the east.}$ $\text{What are the electric and magnetic fields in the room?}$

Options:

1. $\frac{M a_0}{e} \text{ west, } \frac{M a_0}{e v_0} \text{ up}$
2. $\frac{M a_0}{e} \text{ west, } \frac{2M a_0}{e v_0} \text{ down}$
3. $\frac{M a_0}{e} \text{ east, } \frac{2M a_0}{e v_0} \text{ up}$
4. $\frac{M a_0}{e} \text{ east, } \frac{3M a_0}{e v_0} \text{ down}$

Solution:

$\text{Case 1:}$ $a_0 \rightarrow \frac{m a_0}{e} = e E$ $E = \frac{m a_0}{e} \text{ (east)}$ $\text{Case 2:}$ $v_0 \uparrow$ $3 a_0 \rightarrow$ $\text{Net force} = \vec{F}_{\text{electric}} + \vec{F}_{\text{mag}}$ $3 m a_0 = e E + e v_0 B$ $B = \frac{2 m a_0}{e v_0} \text{ (upward)}$ $\text{Magnetic force} = q \left( \vec{V} \times \vec{B} \right) \text{ gives direction of magnetic field } \vec{B}.$

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
}