Welcome to this series on Objective Physics Question Bank for NTA NEET, JEE Mains & WBJEE aspirants! The present section contains a list of the most important and conceptual physics MCQs on the topic Magnetic Force on a Charged Particle or "Motion of Charged Particle in Uniform Magnetic Field" of the chapter Magnetic Effect of Electric Current. This topic includes following subtopics/contents:
2. An electron is moving under the influence of a magnetic field (not necessarily uniform) alone. Its kinetic energy
4. Which of the following particles will experience maximum magnetic force, when projected with the same velocity perpendicular to a uniform magnetic field?
5. Which of the following particles has maximum frequency of rotation in uniform transverse magnetic field?
6. If an electron enters a magnetic field with its velocity pointing along the direction of the magnetic field then:
7. An electron moves with velocity v in a uniform transverse magnetic field B on circular path of radius r. Then, the ratio e/m for it is
8. In a region a uniform magnetic field exists in horizontal plane towards north. If cosmic particles (having 80% protons) are falling vertically downwards, then they are deflected towards
10. A point mass having charge q enters a uniform and transverse magnetic field of induction B with a momentum p. The particle will describe a circular arc with radius equal to
12. An electron is moving with velocity (2i + 3j) m/s in a magnetic field 2k Tesla at some instant. The trajectory of the electron is a
13. A charged particle of mass m and kinetic energy E moves in a uniform magnetic field B perpendicularly. Its frequency of circular motion will be:
14. A proton and an alpha particle enter a uniform transverse magnetic field with the same speed. If the proton takes 25 µs to complete 5 revolutions, then the periodic time for the α- particle will be
15. The instantaneous acceleration of an electron in a magnetic field B = 2i + 3j + 4k is a = xi + j - k. The value of x is:
16. An electron is moving with velocity (2i + 3k) m/s in a magnetic field 2k Tesla at some instant. The trajectory of the electron is a
20. Two electrons A and B move in circles under the influence of a uniform transverse magnetic field with speeds v and 2v respectively. The ratio of their time periods is:
1. D The dimensions of magnetic induction can be obtained from the formula of magnetic force F = qvBsinθ. From this B = F/qvsinθ, so the dimensional formula [B] = [MT⁻²I⁻¹].
3. C The SI unit of magnetic induction can be obtained from the formula of magnetic force F = qvBsinθ. From this B = F/qvsinθ, so the SI unit of B is kilogram per coulomb second (which is also known as tesla).
8. C Magnetic force on protons will be given by F = qv × B. The direction of F can be obtained by the right hand rule. Put the fingers of right palm along the direction of v (vertically downward) and curl them towards B (north). The stretched thumb in this position will represent the direction of magnetic force F (east), as the protons are positively charged particles.
9. A Magnetic force acting on the charged particle is always perpendicular to the instantaneous velocity and therefore each small displacement is perpendicular to the instantaneous magnetic force. Hence work performed by the magnetic field is zero in any time interval.
10. D Magnetic force takes the role of centripetal force. Mathematically qvB =mv²/r or, r = mv/qB = p/qB.
11. D Magnetic Force on a particle moving along the direction of magnetic field is F = qvBsin0° = 0.
12. A Velocity of the electron is perpendicular to the uniform magnetic field. Hence, the electron follows a circular trajectory.
13. B Frequency of rotation of a charged particle in uniform transverse magnetic field is independent of its kinetic energy and is given by f = 1/T = qB/2Ï€m.
14. C Time period of revolutions made by proton = 25 μs/5 = 5 μs. Also from the expression T = 2Ï€m/qB, we have T ∝ m/q. Use this proportionality relation to get the periodic time of alpha particle.
15. A Instantaneous acceleration should always be perpendicular to the magnetic field (this is because the magnetic force acts perpendicular to the magnetic field), therefore simply make the dot product of acceleration and magnetic induction equal to zero i.e. a.B = 0 to evaluate x.
16. B One of the components of the electrons' velocity is parallel to the magnetic field which tends to make it move in a straight line path whereas the other component is normal to the direction of magnetic field providing a circular nature too. The resultant would be a helical trajectory.
17. B Alpha particle is a positively charged particle and therefore it cannot follow the paths C and D. Path C is an undeviated straight track & only a neutral particle (say neutron) can describe it. Path D must be followed by a negatively charged particle (say an electron) as magnetic force acts opposite to v × B.
The remaining two paths A and B are described by positively charged particles like proton and alpha particle. Observing the relative curvature of these two tracks, we can identify the one followed by alpha particle.
Radius of the arc described by a charged particle in uniform transverse magnetic field is r = mv/qB. So when multiple charged particles are projected in same magnetic field with equal velocities, radii of curvature of the tracks described by them are purely dependent upon the respective specific charges (the q/m ratio). Greater the value of q/m, smaller will be the radius of curvature (or more will be the curvature).
Since the ratio q/m is smaller for an alpha particle than a proton; therefore radius described by the alpha particle will be greater (than that by the proton). Hence, path B is of alpha particle.
18. B Time period of the helical motion executed by the particle is given by T = 2Ï€m/qB = 2Ï€(1)/(1)(1) = 2Ï€. And pitch = distance travelled along magnetic field in one periodic time, P = vâ‚—â‚—T = (1cos30°)(2Ï€) = √(3)Ï€.
19. A The proton describes a helical path, and therefore its velocity repeats after every period T = 2Ï€m/eB.
20. C Time period of circular motion executed by a point charge in uniform transverse magnetic field is given by T = 2Ï€m/qB. This expression suggests that, time period is independent of speed. Hence irrespective of their speeds, the two electrons will execute circular motions with equal time periods. In other words, ratio of time periods is 1 : 1.
- Expression of force on a point Charge (moving) in magnetic field
- Motion of Charged Particle parallel and anti-parallel to the magnetic field
- Circular motion of a charged particle in a uniform, transverse magnetic field
- Helical Motion of a Charged Particle in uniform magnetic field
Special care has been taken in selection of problems to ensure that they fall under the syllabus prescribed by the authorities and of the right difficulty level as demanded by the said exams. In fact a fair portion of questions are directly taken from the archives of these exams. This makes this series even more useful and relevant for the students to be used as a DPP (daily practice problems) or regular assignments.
OBJECTIVE QUESTION BANK
Out of the four different choices following each question, only one is the correct (or the most appropriate) which you have to identify and mark.
1. Identify the correct dimensional formula of magnetic induction from the following:
- A) ML⁻²T²I
B) M⁻¹L⁻³T⁴I²
C) MLT⁻²I
D) None of these
2. An electron is moving under the influence of a magnetic field (not necessarily uniform) alone. Its kinetic energy
- A) increases
B) decreases
C) does not change
D) may change or remain constant depending upon whether the field is uniform or not.
3. Which of the following is the SI unit of magnetic induction?
- A) weber/meter
B) gauss
C) kg per coulomb second
D) none of these
4. Which of the following particles will experience maximum magnetic force, when projected with the same velocity perpendicular to a uniform magnetic field?
- A) electron
B) proton
C) He⁺
D) Li⁺⁺
5. Which of the following particles has maximum frequency of rotation in uniform transverse magnetic field?
- A) proton
B) alpha particle
C) electron
D) neutron
6. If an electron enters a magnetic field with its velocity pointing along the direction of the magnetic field then:
- A) the electron will turn towards right
B) the electron will turn towards left
C) the velocity of the electron will change
D) the velocity of the electron will remain unchanged
7. An electron moves with velocity v in a uniform transverse magnetic field B on circular path of radius r. Then, the ratio e/m for it is
- A) v/Br
B) B/rv
C) Bvr
D) vr/B
8. In a region a uniform magnetic field exists in horizontal plane towards north. If cosmic particles (having 80% protons) are falling vertically downwards, then they are deflected towards
- A) north
B) south
C) east
D) west
9. A particle of mass m and charge q moving with a velocity v describes a circle of radius R when subjected to a transverse magnetic field B. What is the work done by the field when the particle completes one full circle?
- A) zero
B) 2BqπR
C) BqπR
D) 2BqvπR
10. A point mass having charge q enters a uniform and transverse magnetic field of induction B with a momentum p. The particle will describe a circular arc with radius equal to
- A) 1.5p/qB
B) 2p/qB
C) p/2qB
D) p/qB
11. A charged particle is moving along the direction of a magnetic field. The magnetic force experienced by the particle
- A) is in the direction of its velocity
B) is directed opposite to its velocity
C) is perpendicular to its velocity
D) is zero
12. An electron is moving with velocity (2i + 3j) m/s in a magnetic field 2k Tesla at some instant. The trajectory of the electron is a
- A) circle
B) straight line
C) helix
D) ellipse
13. A charged particle of mass m and kinetic energy E moves in a uniform magnetic field B perpendicularly. Its frequency of circular motion will be:
- A) qB/Ï€m
B) qB/2Ï€m
C) 2Ï€m/qB
D) none of these
14. A proton and an alpha particle enter a uniform transverse magnetic field with the same speed. If the proton takes 25 µs to complete 5 revolutions, then the periodic time for the α- particle will be
- A) 50 μs
B) 25 μs
C) 10 μs
D) 5 μs
15. The instantaneous acceleration of an electron in a magnetic field B = 2i + 3j + 4k is a = xi + j - k. The value of x is:
- A) 0.5
B) 1
C) 2.5
D) 1.5
16. An electron is moving with velocity (2i + 3k) m/s in a magnetic field 2k Tesla at some instant. The trajectory of the electron is a
- A) circle
B) helix
C) straight line
D) ellipse
17. An electron, a proton, a neutron and an alpha particle enter uniform magnetic field with equal velocities. Identify which of these tracks followed are by alpha particle.
- A) A
B) B
C) C
D) D
18. A particle with charge of 1 C, mass 1 kg and speed 1 m/s enters a uniform magnetic field of induction 1 T, at an angle of 30° between velocity vector and magnetic induction. The pitch of its helical path is (in meters):
- A) √(3)Ï€/2
B) √(3)Ï€
C) π/2
D) π
19. A proton is launched with velocity v in a uniform magnetic field B. The angle θ between v and B lies between 0° and 90°. Its velocity vector v returns to its initial value in a minimum time interval of
- A) 2Ï€m/eB
B) 4Ï€m/eB
C) πm/eB
D) None of these
20. Two electrons A and B move in circles under the influence of a uniform transverse magnetic field with speeds v and 2v respectively. The ratio of their time periods is:
- A) 1 : 2
B) 2 : 1
C) 1 : 1
D) None of these
ANSWERS WITH HINTS
1. D The dimensions of magnetic induction can be obtained from the formula of magnetic force F = qvBsinθ. From this B = F/qvsinθ, so the dimensional formula [B] = [MT⁻²I⁻¹].
2. C Magnetic force on a charged particle always acts perpendicular to its instantaneous velocity, therefore magnitude of velocity (i.e. speed and hence kinetic energy) cannot change.
3. C The SI unit of magnetic induction can be obtained from the formula of magnetic force F = qvBsinθ. From this B = F/qvsinθ, so the SI unit of B is kilogram per coulomb second (which is also known as tesla).
4. D The magnetic force on a charged particle projected perpendicular to a uniform magnetic field is given by F = qvBsin90° = qvB. If v and B are same for all the particles, the one having maximum q will experience the maximum force.
5. C Frequency of rotation of charged particles in uniform, transverse magnetic field is given by f = 1/T = qB/2Ï€m. Therefore, the one having maximum specific charge (the q/m ratio) will rotate with maximum frequency.
6. D Force on an electron moving along the direction of magnetic field is F = qvBsin0° = 0.
In absence of force, the electrons' velocity will remain unchanged.
In absence of force, the electrons' velocity will remain unchanged.
7. A Radius of the circular path is r = mv/eB. This yields e/m = v/Br.
9. A Magnetic force acting on the charged particle is always perpendicular to the instantaneous velocity and therefore each small displacement is perpendicular to the instantaneous magnetic force. Hence work performed by the magnetic field is zero in any time interval.
10. D Magnetic force takes the role of centripetal force. Mathematically qvB =mv²/r or, r = mv/qB = p/qB.
11. D Magnetic Force on a particle moving along the direction of magnetic field is F = qvBsin0° = 0.
12. A Velocity of the electron is perpendicular to the uniform magnetic field. Hence, the electron follows a circular trajectory.
13. B Frequency of rotation of a charged particle in uniform transverse magnetic field is independent of its kinetic energy and is given by f = 1/T = qB/2Ï€m.
14. C Time period of revolutions made by proton = 25 μs/5 = 5 μs. Also from the expression T = 2Ï€m/qB, we have T ∝ m/q. Use this proportionality relation to get the periodic time of alpha particle.
15. A Instantaneous acceleration should always be perpendicular to the magnetic field (this is because the magnetic force acts perpendicular to the magnetic field), therefore simply make the dot product of acceleration and magnetic induction equal to zero i.e. a.B = 0 to evaluate x.
16. B One of the components of the electrons' velocity is parallel to the magnetic field which tends to make it move in a straight line path whereas the other component is normal to the direction of magnetic field providing a circular nature too. The resultant would be a helical trajectory.
17. B Alpha particle is a positively charged particle and therefore it cannot follow the paths C and D. Path C is an undeviated straight track & only a neutral particle (say neutron) can describe it. Path D must be followed by a negatively charged particle (say an electron) as magnetic force acts opposite to v × B.
The remaining two paths A and B are described by positively charged particles like proton and alpha particle. Observing the relative curvature of these two tracks, we can identify the one followed by alpha particle.
Radius of the arc described by a charged particle in uniform transverse magnetic field is r = mv/qB. So when multiple charged particles are projected in same magnetic field with equal velocities, radii of curvature of the tracks described by them are purely dependent upon the respective specific charges (the q/m ratio). Greater the value of q/m, smaller will be the radius of curvature (or more will be the curvature).
Since the ratio q/m is smaller for an alpha particle than a proton; therefore radius described by the alpha particle will be greater (than that by the proton). Hence, path B is of alpha particle.
18. B Time period of the helical motion executed by the particle is given by T = 2Ï€m/qB = 2Ï€(1)/(1)(1) = 2Ï€. And pitch = distance travelled along magnetic field in one periodic time, P = vâ‚—â‚—T = (1cos30°)(2Ï€) = √(3)Ï€.
19. A The proton describes a helical path, and therefore its velocity repeats after every period T = 2Ï€m/eB.
20. C Time period of circular motion executed by a point charge in uniform transverse magnetic field is given by T = 2Ï€m/qB. This expression suggests that, time period is independent of speed. Hence irrespective of their speeds, the two electrons will execute circular motions with equal time periods. In other words, ratio of time periods is 1 : 1.
Tags:
Question Bank