motion of charge particle in magnetic field questions with solutions

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• IntegermediumMagnetic effect of currentmotion of charge particle in magnetic field

  A particle of mass 5 mg and charge 5π×10⁻⁶ C moves with velocity v = (3î+2k̂)×10⁻² m·s⁻¹ in a uniform magnetic field B = 0.1k̂ T. The particle follows a helical path. How far does it move in the +k̂ direction while completing 5 revolutions? Give the answer in metres.

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  JEE Mains 2026 8 April Evening Shift

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• MCQmediumMagnetic effect of currentmotion of charge particle in magnetic field

  A particle of charge 10⁻⁹ C moves in the x-y plane. At a certain instant, the electric field is E = 0.4ĵ N·C⁻¹ and the magnetic field is B = 4×10⁻³ k̂ T. The total electromagnetic force on the particle is F = (4î+2ĵ)×10⁻¹⁰ N. What is the velocity of the particle at that instant?

  Options

  • Option A

    (50î+100ĵ) m·s⁻¹

  • Option B

    (100î+50ĵ) m·s⁻¹

  • Option C

    (-50î+100ĵ) m·s⁻¹

  • Option D

    (50î-100ĵ) m·s⁻¹

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  JEE Mains 2026 2 April Evening Shift

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• MCQmediumMagnetic effect of currentmotion of charge particle in magnetic field

  Two uniform magnetic fields B₁ and B₂, both perpendicular to the plane of the paper, occupy adjacent regions separated by a straight interface as shown in the original figure. A particle of mass m and charge q starts at the interface with speed v, enters region 2, returns to the interface, then moves through region 1 and reaches the interface again. Given B₂ > B₁, the displacement along the interface is:

  

  Options

  • Option A

    (2mv/qB₁)(1-B₂/B₁)

  • Option B

    (mv/qB₁)(1-B₁/B₂)

  • Option C

    (mv/qB₁)(1-B₂/B₁)

  • Option D

    (2mv/qB₁)(1-B₁/B₂)

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  JEE Mains 2025 7 April Morning Shift

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• MCQmediumMagnetic effect of currentmotion of charge particle in magnetic field

  A particle of charge q and mass m is projected from the origin with initial velocity v = (v₀/√2)î+(v₀/√2)ĵ. The region 0 ≤ x ≤ L contains a uniform magnetic field B = B₀ k̂ and a position-dependent electric field E = E₀ exp(-λx) î, where λ is a positive constant. After the particle moves from x = 0 to x = L, what is the change in its kinetic energy?

  Options

  • Option A

    (qE₀/ λ)[1-exp(-λL)]

  • Option B

    (v₀qB₀ /2λ)[2-exp(-2λL)]

  • Option C

    -(qE₀ /λ)[1+exp(-λL)]

  • Option D

    q[(E₀+v₀B₀) /λ][1-exp(-λL /2)]

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  JEE Mains 2026 5 April Evening Shift

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• Multi-correctmediumMagnetic effect of currentmotion of charge particle in magnetic field

  In a vacuum chamber, a particle of charge 1 μC and mass 1 mg is projected with a velocity (î + 2ĵ) m s⁻¹ from the XZ plane at time t = 0 in an electric field of 1î V m⁻¹. At t = 0.2 s, the electric field is switched off and a magnetic field of 6ĵ T is switched on. The acceleration due to gravity is -10ĵ m s⁻². Correct option(s) is/are:

  Select all that apply

  • Option A

    The vertical distance of the particle from the XZ plane at t = 0.3 s is 15 cm.

  • Option B

    The vertical distance of the particle from the XZ plane at t = 0.4 s is 10 cm.

  • Option C

    The radius of the trajectory of the particle for t > 0.2 s is 20 cm.

  • Option D

    The particle will be in the XZ plane at t = 0.35 s.

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  JEE Advanced2026Paper 2

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• IntegereasyMagnetic effect of currentmotion of charge particle in magnetic field

  A charged particle moves in a uniform magnetic field B = (3î+2ĵ) T. Its acceleration is a = [4î-(x /2)ĵ] m·s⁻². Since the magnetic force is perpendicular to the magnetic field, find x.

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  JEE Mains 2026 5 April Morning Shift

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• NumericmediumMagnetic effect of currentmotion of charge particle in magnetic field

  An electron with kinetic energy 5 eV enters a region of uniform magnetic field of 3 μT perpendicular to its direction. An electric field E is applied perpendicular to the direction of velocity and magnetic field. The value of E, so that electron moves along the same path, is_______ N C⁻¹. (Given, mass of electron = 9 × 10⁻³¹ kg, electric charge = 1.6 × 10⁻¹⁹ C)

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  JEE Mains 2024 08 Apr Morning Shift

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• NumericmediumMagnetic effect of currentmotion of charge particle in magnetic field

  An electron moves through a uniform magnetic field $\vec{B}$= B₀î + 2B₀ĵ T. At a particular instant, the velocity of the electron is $\vec{V}$= 3î + 5ĵ m s⁻¹. If the magnetic force acting on the electron is $\vec{F}$= 5e k̂ N, where e is the magnitude of charge of electron, then the value of B₀ is ____ T.

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  JEE Mains 2024 31 Jan Morning Shift

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• NumericeasyMagnetic effect of currentmotion of charge particle in magnetic field

  A charge of 4.0 μC is moving with a velocity of 4.0 × 10⁶ ms⁻¹ along the positive y-axis under a magnetic field $\vec{B}$ of strength (2k̂) T. The force acting on the charge is xî N. The value of x is __.

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  JEE Mains 2024 29 Jan Evening Shift

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• MCQeasyMagnetic effect of currentmotion of charge particle in magnetic field

  The electrostatic force F₁ and magnetic force F₂ acting on a charge q moving with velocity V can be written :

  Options

  • Option A

    F₁ = q(V · E), F₂ = q(B · V)

  • Option B

    F₁ = qB, F₂ = q(B × V)

  • Option C

    F₁ = qE, F₂ = q(V × B)

  • Option D

    F₁ = qE, F₂ = q(B × V)

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  JEE Mains 2024 05 Apr Evening Shift

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