Q. No.
A charged particle moves in a circular path of radius \(r\) in a uniform magnetic field \(B,\) perpendicular to the plane of motion. The same particle is observed to move in a circular path around an infinite line charge \(\lambda\) (charge/unit length), moving with the same kinetic energy as before. The charge to mass ratio of the particle is proportional to:
1.
\(\lambda Br\)
2.
\(\dfrac{\lambda Br}{r}\)
3.
\(\dfrac{\lambda}{Br}\)
4.
\(\dfrac{\lambda}{B^2r^2}\)
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| 1. | \(\dfrac{q^2\phi}{2m}\) | 2. | \(\dfrac{q^2\phi}{2\pi m}\) |
| 3. | \(\dfrac{q^2\phi}{m}\) | 4. | \(\dfrac{q^2\phi}{\pi m}\) |
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Which of the following is the possible magnetic field (in tesla)?
1. \(2\hat j\)
2. \(2\hat k\)
3. \(2\hat i+2\hat k\)
4. \(2\hat j+2\hat k\)
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| 1. | \(\dfrac{5}{\sqrt3r}\) | 2. | \(\dfrac{5}{\sqrt3\pi r}\) |
| 3. | \(\dfrac{5}{r}\) | 4. | \(\dfrac{5}{\pi r}\) |
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| 1. | a resistance of \(25~\Omega\) in series |
| 2. | a resistance of \(\dfrac1{25}~\Omega\) in series |
| 3. | a resistance of \(25~\Omega\) in parallel |
| 4. | a resistance of \(\dfrac1{25}~\Omega\) in parallel |
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| 1. | \(q\Phi\) | 2. | \(\dfrac{q\Phi}{2\pi}\) |
| 3. | \(\pi q\Phi\) | 4. | \(\dfrac{q\Phi}{\pi}\) |
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1. \(0.1\) mA
2. \(0.2\) mA
3. \(1\) mA
4. \(2\) mA
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| (I) | at two adjacent vertices \(A,B\) |
| (II) | at two points \(A,C\) at the ends of a diagonal. |
| 1. | \(2\) | 2. | \(\dfrac12\) |
| 3. | \(\dfrac{1}{\sqrt2}\) | 4. | \(1\) |
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| 1. | \(\dfrac{q^2B}{2\pi m}\) | 2. | \(\dfrac{qB^2}{m}\) |
| 3. | \(\dfrac{2\pi m}{q^2B}\) | 4. | \(\dfrac{qB}{m^2}\) |
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| 1. | \(2\) | 2. | \(\dfrac43\) |
| 3. | \(\dfrac32\) | 4. | \(4\) |
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