Motion of Charged Particle In Magnetic Field and Lorentz Force PYQs: JEE Mains Physics

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1. 1. \(1\,\mu\)C charge moving with velocity \(\vec{v} = \left(\hat{i} - 2\hat{j} + 3\hat{k}\right)\) m/s in the region of magnetic field \(\vec{B} = \left(2\hat{i} + 3\hat{j} - 5\hat{k}\right)\) T. The magnitude of force acting on it is \(\sqrt{\alpha} \times 10^{-6}\) N. The value of \(\alpha\) is _______. 2026 Medium
2. 2. A \(5\) mg particle carrying a charge of \(5\pi\times 10^{-6}\) C is moving with velocity of \((3\hat{i}+2\hat{k})\times 10^{-2}\) m/s in a region having magnetic field \(\vec{B} = 0.1\hat{k}\) Wb/m\(^2\). It moves a distance of \(\alpha\) meter along \(\hat{k}\) when it completes \(5\) revolutions. The value of \(\alpha\) is ________. 2026 Hard
3. 3. A current carrying 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 : 2026 Easy
4. 4. A particle having charge \(10^{-9}\) C moving in \(x\)-\(y\) plane in fields of \(0.4\hat{j}\) N/C and \(4 \times 10^{-3} \hat{k}\) T experiences a force of \((4\hat{i} + 2\hat{j}) \times 10^{-10}\) N. The velocity of the particle at that instant is _______ m/s. 2026 Hard
5. 5. A particle of charge \(1.6 \mu \mathrm{C}\) and mass \(16 \mu \mathrm{~g}\) is present in a strong magnetic field of 6.28 T. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is ________ S. \((\pi=3.14)\) 2025 Easy
6. 6. A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of \(2 \times 10^5 \mathrm{~ms}^{-1}\). When the electric field is switched off, the proton moves along a circular path of radius 2 cm . The magnitude of electric field is \(x \times 10^4 \mathrm{~N} / \mathrm{C}\). The value of \(x\) is _______ Take the mass of the proton \(=1.6 \times 10^{-27} \mathrm{~kg}\). 2025 Hard
7. 7. A tightly wound long solenoid carries a current of 1.5 A . An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns . The number of turns per metre in the solenoid is ________.
   [Take mass of electron \(\mathrm{m}_{\mathrm{e}}=9 \times 10^{-31} \mathrm{~kg}\), charge of electron \(\left|\mathrm{q}_{\mathrm{e}}\right|=1.6 \times 10^{-19} \mathrm{C}\),
   \(\left.\mu_0=4 \pi \times 10^{-7} \frac{\mathrm{~N}}{\mathrm{~A}^2}, 1 \mathrm{~ns}=10^{-9} \mathrm{~s}\right]\) 2025 Easy
8. 8. Consider a long thin conducting wire carrying a uniform current I. A particle having mass " M " and charge " \(q\) " is released at a distance " \(a\) " from the wire with a speed \(v_0\) along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance \(x\) from the wire. The value of \(x\) is [ \(\mu_0\) is vacuum permeability] 2025 Hard
9. 9. Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
   Assertion (A) : A electron in a certain region of uniform magnetic field is moving with constant velocity in a straight line path.
   Reason (R): The magnetic field in that region is along the direction of velocity of the electron. In the light of the above statements, choose the correct answer from the options given below : 2025 Medium
10. 10. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R .
    Assertion A : If oxygen ion \(\left(\mathrm{O}^{-2}\right)\) and Hydrogen ion \(\left(\mathrm{H}^{+}\right)\)enter normal to the magnetic field with equal momentum, then the path of \(\mathrm{O}^{-2}\) ion has a smaller curvature than that of \(\mathrm{H}^{+}\).
    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.
    In the light of the above statements, choose the correct answer from the options given below : 2025 Easy
11. 11. Uniform magnetic fields of different strengths \(\left(B_1\right.\) 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 \(B_2 \gt B_1\)) 2025 Easy
12. 12. A proton and a deutron ( \(\mathrm{q}=+\mathrm{e}, m=2.0 \mathrm{u})\) having same kinetic energies enter a region of uniform magnetic field \(\vec{B}\), moving perpendicular to \(\vec{B}\). The ratio of the radius \(r_d\) of deutron path to the radius \(r_p\) of the proton path is _______. 2024 Hard
13. 13. An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then : 2024 Hard
14. 14. An electron moves through a uniform magnetic field \(\vec{B}=B_0 \hat{i}+2 B_0 \hat{j} T\). At a particular instant of time, the velocity of electron is \(\overrightarrow{\mathrm{u}}=3 \hat{i}+5 \hat{j} \mathrm{~m} / \mathrm{s}\). If the magnetic force acting on electron is \(\vec{F}=5 e\hat kN\), where \(e\) is the charge of electron, then the value of \(\mathrm{B}_0\) is _______\(\mathrm{T}\). 2024 Hard
15. 15. An electron with kinetic energy \(5 \mathrm{eV}\) enters a region of uniform magnetic field of \(3 \mu \mathrm{T}\) perpendicular to its direction. An electric field \(\mathrm{E}\) is applied perpendicular to the direction of velocity and magnetic field. electron moves along the same path, The value of \(\mathrm{E}\) is _______ \(\mathrm{NC}^{-1}\). (Given, mass of electron \(=9 \times 10^{-31} \mathrm{~kg}\), electric charge \(=1.6 \times 10^{-19} \mathrm{C}\) ) 2024 Hard
16. 16. The electrostatic force \(\left(\vec{F}_1\right)\) and magnetic force \(\left(\vec{F}_2\right)\) acting on a charge \(q\) moving with velocity \(v\) can be written _______. 2024 Hard
17. 17. Two particles \(\mathrm{X}\) and \(\mathrm{Y}\) having equal charges are being accelerated through the same potential difference. Thereafter they enter normally in a region of uniform magnetic field and describes circular paths of radius \(R_1\) and \(R_2\) respectively. The mass ratio of \(\mathrm{X}\) and \(\mathrm{Y}\) is _______. 2024 Medium
18. 18. A charge particle moving in magnetic field \(B\), has the components of velocity along \(B\) as well as perpendicular to \(B\). The path of the charge particle will be 2023 Medium
19. 19. A charge particle of \(2\,\mu\,C\) accelerated by a potential difference of \(100\,V\) enters a region of uniform magnetic field of magnitude \(4\,m\,T\) at right angle to the direction of field. The charge particle completes semicircle of radius \(3\,cm\) inside magnetic field. The mass of the charge particle is \(........\times 10^{-18}\,kg\). 2023 Medium
20. 20. A proton with a kinetic energy of \(2.0\,eV\) moves into a region of uniform magnetic field of magnitude \(\frac{\pi}{2} \times 10^{-3}\,T\). The angle between the direction of magnetic field and velocity of proton is \(60^{\circ}\). The pitch of the helical path taken by the proton is \(..........cm\) (Take, mass of proton \(=1.6 \times 10^{-27}\,kg\) and Charge on proton \(=1.6 \times 10^{-19}\,kg)\) 2023 Medium
21. 21. An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid. \(A.\) The electron will experience magnetic force along the axis of the solenoid. \(B.\) The electron will not experience magnetic force. \(C.\) The electron will continue to move along the axis of the solenoid. \(D.\) The electron will be accelerated along the axis of the solenoid. \(E.\) The electron will follow parabolic path-inside the solenoid. Choose the correct answer from the options given below: 2023 Medium
22. 22. An electron is moving along the positive \(x\)-axis. If the uniform magnetic field is applied parallel to the negative \(z\)-axis. then \(A.\) The electron will experience magnetic force along positive \(y\)-axis \(B.\) The electron will experience magnetic force along negative \(y\)-axis \(C.\) The electron will not experience any force in magnetic field \(D.\) The electron will continue to move along the positive \(x\)-axis \(E.\) The electron will move along circular path in magnetic field Choose the correct answer from the options given below: 2023 Medium
23. 23. The magnetic moments associated with two closely wound circular coils \(A\) and \(B\) of radius \(r_A=10 cm\) and \(r_B=20 cm\) respectively are equal if: (Where \(N _A, I _{ A }\) and \(N _B, I _{ B }\) are number of turn and current of \(A\) and \(B\) respectively) 2023 Medium
24. 24. A charge particle is moving in a uniform magnetic field \((2 \hat{i}+3 \hat{j}) T\). If it has an acceleration of \((\alpha \hat{i}-4 \hat{j}) m / s ^{2}\), then the value of \(\alpha\) will be. 2022 Hard
25. 25. A charged particle moves along circular path in a uniform magnetic field in a cyclotron. The kinetic energy of the charged particle increases to \(4\) times its initial value. What will be the ratio of new radius to the original radius of circular path of the charged particle 2022 Medium
26. 26. A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If \(r_{d}\) and \(r_{p}\) are the radii of their circular paths respectively, then the ratio \(\frac{r_{d}}{r_{p}}\) will be \(\sqrt{ x }: 1\) where \(x\) is .......... 2022 Medium
27. 27. A proton, a deuteron and an \(\alpha-\)particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is 2022 Medium
28. 28. A singly ionized magnesium atom \((A=24)\) ion is accelerated to kinetic energy \(5\,keV\) and is projected perpendicularly into a magnetic field \(B\) of the magnitude \(0.5\,T\). The radius of path formed will be___________ \(cm\) 2022 Medium
29. 29. An electron with energy \(0.1\,ke\,V\) moves at right angle to the earth's magnetic field of \(1 \times 10^{-4}\,Wbm ^{-2}\). The frequency of revolution of the electron will be. (Take mass of electron \(=9.0 \times 10^{-31}\,kg\) ) 2022 Easy
30. 30. Given below are two statements: One is labelled as Assertion \((A)\) and the other is labelled as Reason \((R).\) Assertion \((A)\) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle. Reason \((R)\) : Moving charged particle experiences magnetic force perpendicular to its direction of motion. 2022 Medium
31. 31. Given below are two statements Statement \(I\) : The electric force changes the speed of the charged particle and hence changes its kinetic energy: whereas the magnetic force does not change the kinetic energy of the charged particle Statement \(II\) : The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field. In the light of the above statements, choose the most appropriate answer from the options given below 2022 Medium
32. 32. Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is \(6: 5\) and their respective masses ratio is \(9: 4\). Then, the ratio of their charges will be. 2022 Medium
33. 33. Two long parallel conductors \(S_{1}\) and \(S_{2}\) are separated by a distance \(10 \,cm\) and carrying currents of \(4\, A\) and \(2 \,A\) respectively. The conductors are placed along \(x\)-axis in \(X - Y\) plane. There is a point \(P\) located between the conductors (as shown in figure). A charge particle of \(3 \pi\) coulomb is passing through the point \(P\) with velocity \(\overrightarrow{ v }=(2 \hat{ i }+3 \hat{ j }) \,m / s\); where \(\hat{i}\) and \(\hat{j} \quad\) represents unit vector along \(x\) and \(y\) axis respectively. The force acting on the charge particle is \(4 \pi \times 10^{-5}(-x \hat{i}+2 \hat{j}) \,N\). The value of \(x\) is
    2022 Hard
34. 34. A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let \(r_{d}\) and \(r_{\alpha}\) be their respective radii of circular path. The value of \(\frac{r_{d}}{r_{\alpha}}\) is equal to 2021 Medium
35. 35. A proton, a deuteron and an \(\alpha\) particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is.......... and their speed is.................. in the ratio. 2021 Hard
36. 36. A proton and an \(\alpha\) -particle, having kinetic energies \(K _{ p }\) and \(K _{\alpha},\) respectively, enter into \(a\) magnetic field at right angles. The ratio of the radii of trajectory of proton to that of \(\alpha\) -particle is \(2: 1 .\) The ratio of \(K _{ p }: K _{\alpha}\) is : 2021 Medium
37. 37. Two ions having same mass have charges in the ratio \(1: 2\). They are projected normally in a uniform magnetic field with their speeds in the ratio \(2: 3\). The ratio of the radii of their circular trajectories is - 2021 Medium
38. 38. Two ions of masses \(4 \,{amu}\) and \(16\, amu\) have charges \(+2 {e}\) and \(+3 {e}\) respectively. These ions pass through the region of constant perpendicular magnetic field. The kinetic energy of both ions is same. Then : 2021 Hard
39. 39. A beam of protons with speed \(4 \times 10^{5}\, ms ^{-1}\) enters a uniform magnetic field of \(0.3\, T\) at an angle of \(60^{\circ}\) to the magnetic field. The pitch of the resulting helical path of protons is close to....\(cm\) (Mass of the proton \(=1.67 \times 10^{-27}\, kg\), charge of the proton \(=1.69 \times 10^{-19}\,C\)) 2020 Medium
40. 40. A charged particle carrying charge \(1\,\mu C\) is moving with velocity \((2 \hat{ i }+3 \hat{ j }+4 \hat{ k })\, ms ^{-1} .\) If an external magnetic field of \((5 \hat{ i }+3 \hat{ j }-6 \hat{ k }) \times 10^{-3}\, T\) exists in the region where the particle is moving then the force on the particle is \(\overline{ F } \times 10^{-9} N\). The vector \(\overrightarrow{ F }\) is : 2020 Medium
41. 41. A particle of charge \(q\) and mass \(m\) is moving with a velocity \(-v \hat{ i }(v \neq 0)\) towards a large screen placed in the \(Y - Z\) plane at a distance \(d.\) If there is a magnetic field \(\overrightarrow{ B }= B _{0} \hat{ k },\) the minimum value of \(v\) for which the particle will not hit the screen is 2020 Medium
42. 42. An electron gun is placed inside a long solenoid of radius \(\mathrm{R}\) on its axis. The solenoid has \(\mathrm{n}\) turns/length and carries a current \(I\). The electron gun shoots an electron along the radius of the solenoid with speed \(v\). If the electron does not hit the surface of the solenoid, maximum possible value of \({v}\) is (all symbols have their standard meaning)
    2020 Medium
43. 43. An electron is moving along \(+x\) direction with a velocity of \(6 \times 10^{6}\, ms ^{-1}\). It enters a region of uniform electric field of \(300 \,V / cm\) pointing along \(+ y\) direction. The magnitude and direction of the magnetic field set up in this region such that the electron keeps moving along the \(x\) direction will be 2020 Hard
44. 44. Proton with kinetic energy of \(1\;MeV\) moves from south to north. It gets an acceleration of \(10^{12}\; \mathrm{m} / \mathrm{s}^{2}\) by an applied magnetic field (west to east). The value of magnetic field :.......\(mT\) (Rest mass of proton is \(1.6 \times 10^{-27} \;\mathrm{kg}\) ) 2020 Medium
45. 45. The figure shows a region of length \('l'\) with a uniform magnetic field of \(0.3\, T\) in it and a proton entering the region with velocity \(4 \times 10^{5}\, ms ^{-1}\) making an angle \(60^{\circ}\) with the field. If the proton completes \(10\) revolution by the time it cross the region shown, \(l\) is close to....... \(m\) (mass of proton \(=1.67 \times 10^{-27} \,kg ,\) charge of the proton \(\left.=1.6 \times 10^{-19}\, C \right)\)
    2020 Hard
46. 46. A particle having the same charge as of electron moves in a circular path of radius \(0.5
    \,cm\) under the influence of a magnetic field of \(0.5\,T.\) If an electric field of \(100\,V/m\) makes it to move in a straight path, then the mass of the particle is (given charge of electron \(= 1.6 \times 10^{-19}\, C\) ) 2019 Medium
47. 47. A particle of mass \(m\) and charge \(q\) is in an electric and magnetic field given by \(\vec E = 2\hat i + 3\hat j ;\, B = 4\hat j + 6\hat k\) The charged particle is shifted from the origin to the point \(P(x = 1 ;\, y = 1)\) along a straight path. The magnitude of the total work done is 2019 Medium
48. 48. A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbitals in a plane due to magnetic field perpendicular to the plane. Let \(r_p, r_e\) and \(r_{He}\) be their respective radii, then 2019 Medium
49. 49. A proton and an \(\alpha -\) particle (with their masses in the ratio of \(1 : 4\) and charges in the ratio of \(1:2\) are accelerated from rest through a potential difference \(V\). If a uniform magnetic field \((B)\) is set up perpendicular to their velocities, the ratio of the radii \(r_p : r_{\alpha }\) of the circular paths described by them will be 2019 Medium
50. 50. An electron, moving along the \(x-\) axis with an initial energy of \(100\, eV\), enters a region of magnetic field \(\vec B = (1.5\times10^{-3}T)\hat k\) at \(S\) (See figure). The field extends between \(x = 0\) and \(x = 2\, cm\). The electron is detected at the point \(Q\) on a screen placed \(8\, cm\) away from the point \(S\). The distance \(d\) between \(P\) and \(Q\) (on the screen) is :......\(cm\) (electron's charge \(= 1.6\times10^{-19}\, C\), mass of electron \(= 9.1\times10^{-31}\, kg\))
    2019 Hard

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