Q. No.A circular coil \(ABCD\) carrying a current \(i\) is placed in a uniform magnetic field. If the magnetic force on the segment \(AB\) is \(\vec{ F},\) then the force on the remaining segment \(BCDA\) is:
1. \(-\vec{F}\)
2. \(3\vec{F}\)
3. \(-3\vec{F}\)
4. \(\vec{F}\)
(The charge on electron = \(1.6 \times 10^{-19} ~\text C\) )
1. \(3.2~\text N\)
2. \(3.2 \times 10^{-16} ~\text N\)
3. \(1.6 \times 10^{-16} ~\text N\)
4. zero
A particle having a mass of \(10^{-2}\) kg carries a charge of \(5\times 10^{-8}~\mathrm{C}\). The particle is given an initial horizontal velocity of \(10^5~\mathrm{ms^{-1}}\) in the presence of electric field \(\vec{E}\) and magnetic field \(\vec{B}\) . To keep the particle moving in a horizontal direction, it is necessary that:
| (a) | \(\vec{B}\) should be perpendicular to the direction of velocity and \(\vec{E}\) should be along the direction of velocity. |
| (b) | Both \(\vec{B}\) and \(\vec{E}\) should be along the direction of velocity. |
| (c) | Both \(\vec{B}\) and \(\vec{E}\) are mutually perpendicular and perpendicular to the direction of velocity |
| (d) | \(\vec{B}\) should be along the direction of velocity and \(\vec{E}\) should be perpendicular to the direction of velocity. |
Which one of the following pairs of statements is possible?
| 1. | (c) and (d) |
| 2. | (b) and (c) |
| 3. | (b) and (d) |
| 4. | (a) and (c) |
1. \(1.5\times10^{-3}\) Nm
2. \(1.5\times10^{-2}\) Nm
3. \(3\times10^{-2}\) Nm
4. \(3\times10^{-3}\) Nm
A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in x-z plane. If the current in the loop is I, then the resultant magnetic field due to the two semicircular parts at their common centre is:
1.
2.
3.
4.
A square loop, carrying a steady current \(I,\) is placed in a horizontal plane near a long straight conductor carrying a steady current \(I_1\) at a distance \(d\) from the conductor as shown in the figure. The loop will experience:
| 1. | a net attractive force toward the conductor |
| 2. | a net repulsive force away from the conductor |
| 3. | a net torque acting upward perpendicular to the horizontal plane |
| 4. | a net torque acting downward normal to the horizontal plane |
Charge q is uniformly spread on a thin ring of radius R. The ring rotates about its axis with a uniform frequency of f Hz. The magnitude of magnetic induction at the centre of the ring is:
1.
2.
3.
4.
| 1. | \({G \over (S+G)}\) | 2. | \({S^2 \over (S+G)}\) |
| 3. | \({SG \over (S+G)}\) | 4. | \({G^2 \over (S+G)}\) |
A proton carrying \(1~\text{MeV}\) kinetic energy is moving in a circular path of radius \(R\) in a uniform magnetic field. What should be the energy of an \(\alpha \text- \)particle to describe a circle of the same radius in the same field?
| 1. | \(1~\text{MeV}\) | 2. | \(0.5~\text{MeV}\) |
| 3. | \(4~\text{MeV}\) | 4. | \(2~\text{MeV}\) |
Two circular coils \(1\) and \(2\) are made from the same wire but the radius of the \(1\)st coil is twice that of the \(2\)nd coil. What is the ratio of the potential difference applied across them so that the magnetic field at their centres is the same?
1. \(3\)
2. \(4\)
3. \(6\)
4. \(2\)
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