Q. No.A particle having charge \(10^{-9}~\text{C}\) moving in \(x\text-y\) plane in fields of \(0.4\hat{j}~\text{N/C}\) and \(4\times10^{-3}\hat{k}~\text{T}\) experiences a force of \((4 \hat{\imath}+2 \hat{\jmath}) \times 10^{-10} ~\text{N} .\) The velocity of the particle at that instant is: (in m/s)
1. \(50 \hat{i}+100 \hat{j}\)
2. \(100 \hat{i}+50 \hat{j}\)
3. \(-50 \hat{i}+100 \hat{j}\)
4. \(50 \hat{i}-100 \hat{j}\)
1. \(50 \hat{i}+100 \hat{j}\)
2. \(100 \hat{i}+50 \hat{j}\)
3. \(-50 \hat{i}+100 \hat{j}\)
4. \(50 \hat{i}-100 \hat{j}\)
Subtopic: Lorentz Force |
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\(1~\mu\text{C}\) charge moving with velocity \(\vec{v}=(\hat{i}-2 \hat{j}+3 \hat{k})~ \text{m/s}\) in the region of magnetic field \(\overrightarrow{{B}}=(2 \hat{i}+3 \hat{j}-5 \hat{k})~ \text{T}\). The magnitude of forces acting on it is \(\sqrt{\alpha} \times 10^{-6} ~\text{N} .\) The value of \(\alpha\) is:
1. \(151\)
2. \(161\)
3. \(171\)
4. \(180\)
1. \(151\)
2. \(161\)
3. \(171\)
4. \(180\)
Subtopic: Lorentz Force |
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The charged particle moving in a uniform magnetic field of \((3 \hat{i}+2 \hat{j})~\text{T}\) has an acceleration \(\left(4 \hat{i}-\dfrac{x}{2} \hat{j}\right) \text{m/s}^2 .\) The value of \(x\) is:
1. \(3\)
2. \(4\)
3. \(8\)
4. \(12\)
1. \(3\)
2. \(4\)
3. \(8\)
4. \(12\)
Subtopic: Lorentz Force |
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A \(5~\text{mg}\) particle carrying a charge of \(5 \pi \times 10^{-6} ~\text{C}\) \((3 \hat{i}+2 \hat{k}) \times 10^{-2} ~\text{m/s}\) \(\vec{B}=0.1 \hat{k}~ \text{Wb/m}^2.\) \(\alpha\) \(\alpha\)
1. \(2\)
2. \(5\)
3. \(7\)
4. \(9\)
1. \(2\)
2. \(5\)
3. \(7\)
4. \(9\)
Subtopic: Lorentz Force |
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A current carrying solenoid is placed vertically and a particle of mass \(m\) with charge \(Q\) is released from rest. The particle moves along the axis of solenoid. If \(g\) is acceleration due to gravity then the acceleration \((a)~\) of the charged particle will satisfy:
1. \(a=g~~\)
2. \(a>g~~\)
3. \(a=0~~\)
4. \(0<a<g~~\)
1. \(a=g~~\)
2. \(a>g~~\)
3. \(a=0~~\)
4. \(0<a<g~~\)
Subtopic: Lorentz Force |
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A particle of charge \(1.6 ~\mu \text C\) and mass \(16 ~\mu \text g\) is present in a strong magnetic field of \(6.28 ~\text T.\) The particle is then fired perpendicular to magnetic field. The time required for the particle to return to its original location for the first time is: \((\pi=3.14) \)
1. \(10^{-2}~\text s\)
2. \(10^{-4}~\text s\)
3. \(10^{2}~\text s\)
4. \(10^{4}~\text s\)
1. \(10^{-2}~\text s\)
2. \(10^{-4}~\text s\)
3. \(10^{2}~\text s\)
4. \(10^{4}~\text s\)
Subtopic: Lorentz Force |
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Given below are two statements:
Choose the correct answer from the options given below:
| Assertion(A): | If Oxygen ion \((O^{-2})\) and Hydrogen ion \((H^+)\) enter normal to the magnetic field with equal momentum, then the path of \(O^{-2} \) ion has a smaller curvature than that of \(H^+ .\) |
| Reason(R): | A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Lorentz Force |
Level 4: Below 35%
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A \(4.0 ~\text{cm}\) long straight wire carrying a current of \(8 ~\text{A}\) is placed perpendicular to a uniform magnetic field of strength \(0.15 ~\text{T}.\) The magnetic force on the wire is: (in mN)
1. \(48\)
2. \(30 \)
3. \(26\)
4. \(10\)
1. \(48\)
2. \(30 \)
3. \(26\)
4. \(10\)
Subtopic: Lorentz Force |
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Uniform magnetic field of different strengths (\(B_1\) and \(B_2 \)) both normal to the plane of the paper exist as shown in the figure. A charged particle of mass \(m\) and charge \(q.\) at the interface at an instant, moves into the region \(2\) with velocity \(v\) and returns to the interface. It continues to move into region \(1\) and finally reaches the interface. What is the displacement of the particle during this movement along the interface? (Consider the velocity of the particle to be normal to the magnetic field and \(B_2 > B_1 ~\))
1. \(\dfrac{m v}{{qB}_1}\left(1-\dfrac{{B}_1}{{~B}_2}\right) \)
2. \(\dfrac{m v}{q B_1}\left(1-\dfrac{B_2}{B_1}\right) \)
3. \(\dfrac{{mv}}{{qB}_1}\left(1-\dfrac{{B}_1}{{~B}_2}\right) \times 2 \)
4. \(\dfrac{{mv}}{{qB}_1}\left(1-\dfrac{{B}_2}{{~B}_1}\right) \times 2 \)
1. \(\dfrac{m v}{{qB}_1}\left(1-\dfrac{{B}_1}{{~B}_2}\right) \)
2. \(\dfrac{m v}{q B_1}\left(1-\dfrac{B_2}{B_1}\right) \)
3. \(\dfrac{{mv}}{{qB}_1}\left(1-\dfrac{{B}_1}{{~B}_2}\right) \times 2 \)
4. \(\dfrac{{mv}}{{qB}_1}\left(1-\dfrac{{B}_2}{{~B}_1}\right) \times 2 \)
Subtopic: Lorentz Force |
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A particle of charge \(q,\) mass \(m\) and kinetic energy \(E\) enters in magnetic field perpendicular to its velocity and undergo a circular arc of radius \(r.\) Which of the following curves represents the variation of \(r \) with \(E? ~\)
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Lorentz Force |
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