Q. No.
Moving perpendicular to field \(B\), a proton and an alpha particle both enter an area of uniform magnetic field \(B\). If the kinetic energy of the proton is \(1~\text{MeV}\) and the radius of the circular orbits for both particles is equal, the energy of the alpha particle will be:
1. \(4~\text{MeV}\)
2. \(0.5~\text{MeV}\)
3. \(1.5~\text{MeV}\)
4. \(1~\text{MeV}\)
When a proton is released from rest in a room, it starts with an initial acceleration \(a_0\) towards the east. When it is projected towards the north with a speed of \(v_0\), it moves with an initial acceleration of \(3a_0\) towards the east. What are the electric and magnetic fields in the room?
| 1. | \(\frac{M a_0}{e} ~\text{west,}~ \frac{M a_0}{e v_0}~\text{up}\) |
| 2. | \(\frac{M a_0}{e} ~\text {west,} ~\frac{2 M a_0}{e v_0}~\text{down}\) |
| 3. | \(\frac{M a_0}{e} ~\text{east,} \frac{2 M a_0}{e v_0}~\text{up}\) |
| 4. | \(\frac{M a_0}{e} ~\text {east,} \frac{3 M a_0}{e v_0} ~\text {down}\) |
(Charge on electron = \(1.6 \times 10^{-19} \) C)
1. \(3.2\) N
2. \(3.2 \times 10^{-16} \) N
3. \(1.6 \times 10^{-16} \) N
4. zero
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. \(2~\text{MeV}\)
A uniform electric field and a uniform magnetic field are acting in the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron:
1. speed will decrease
2. speed will increase
3. will turn towards the left of the direction of motion
4. will turn towards the right of the direction of motion
A beam of cathode rays is subjected to cross Electric (E) and magnetic fields(B). The fields are adjusted such that the beam is not deflected. The specific charge of the cathode rays is given by:
1.
2.
3.
4.
(where V is the potential difference between cathode and anode)
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) |
Under the influence of a uniform magnetic field, a charged particle moves with constant speed \(v\) in a circle of radius \(R.\) The time period of rotation of the particle:
| 1. | depends on \(v\) and not on \(R.\) |
| 2. | depends on R and not on \(v.\) |
| 3. | is independent of both \(v\) and \(R.\) |
| 4. | depends on both \(v\) and \(R.\) |
| 1. | 8 N in - z-direction. |
| 2. | 4 N in the z-direction. |
| 3. | 8 N in the y-direction. |
| 4. | 8 N in the z-direction. |
A particle of mass \(m\), charge \(Q\), and kinetic energy \(T\) enters a transverse uniform magnetic field of induction \(\vec B\). What will be the kinetic energy of the particle after seconds?
| 1. | \(3~\text{T}\) | 2. | \(2~\text{T}\) |
| 3. | \(\text{T}\) | 4. | \(4~\text{T}\) |
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