Motion of Charged Particles in a Magnetic Field questions with solutions

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• MCQmediumMagnetic effect of currentMotion of Charged Particles in a Magnetic Field

  A particle of mass 10⁻² kg and charge 5 × 10⁻⁸ C is given a horizontal velocity 10⁵ m/s in electric and magnetic fields. To maintain horizontal motion, which pairs of statements are possible? (I) B⃗ ⟂ v⃗ and E⃗ ∥ v⃗. (II) Both B⃗ and E⃗ are parallel to v⃗. (III) B⃗, E⃗ and v⃗ are mutually perpendicular. (IV) B⃗ ∥ v⃗ and E⃗ ⟂ v⃗.

  Options

  • Option A

    (I) and (III)

  • Option B

    (III) and (IV)

  • Option C

    (II) and (III)

  • Option D

    (II) and (IV)

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  AIPMT Mains 2010NEET Previous Year

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• MCQmediumMagnetic effect of currentMotion of Charged Particles in a Magnetic Field

  A proton and an α-particle enter a uniform magnetic field B at right angles to the field. The radius of the circular orbit is the same for each. If the proton has kinetic energy 1 MeV, what is the kinetic energy of the α-particle?

  Options

  • Option A

    4 MeV

  • Option B

    0.5 MeV

  • Option C

    1.5 MeV

  • Option D

    1 MeV

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  AIPMT July 2015NEET Previous Year

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• NumericmediumMagnetic effect of currentMotion of Charged Particles in a Magnetic Field

  A charged particle of 2 μC, accelerated by a potential difference of 100 V, enters a uniform magnetic field of magnitude 4 mT at right angle to the field. It completes a semicircle of radius 3 cm inside the magnetic field. The mass of the charged particle is _____ × 10⁻¹⁸ kg.

  Your answer

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• MCQmediumMagnetic effect of currentMotion of Charged Particles in a Magnetic Field

  A charged particle passes undeflected through mutually perpendicular uniform electric and magnetic fields. If its velocity is perpendicular to both fields, what is its speed?

  Options

  • Option A

    EB

  • Option B

    E/B

  • Option C

    B/E

  • Option D

    √(E/B)

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  JEE MainsNEET

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• MCQeasyMagnetic effect of currentMotion of Charged Particles in a 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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• Multi-correctmediumMagnetic effect of currentMotion of Charged Particles in a Magnetic Field

  Two charged particles have equal kinetic energies and equal charge magnitudes but different masses. They enter the same uniform magnetic field perpendicularly. Which statements are correct?

  Select all that apply

  • Option A

    Their radii are proportional to √m.

  • Option B

    Their cyclotron periods are proportional to m.

  • Option C

    Their speeds are proportional to 1/√m.

  • Option D

    Their radii are independent of mass.

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• MCQmediumMagnetic effect of currentMotion of Charged Particles in a Magnetic Field

  Assertion (A): If O²⁻ and H⁺ ions enter perpendicular to the same magnetic field with equal momentum, the path of O²⁻ has a smaller radius of curvature than that of H⁺. Reason (R): A proton and an electron having the same momentum form paths of different radii in the same magnetic field because their masses are different. Choose the correct answer.

  Options

  • Option A

    A is true but R is false

  • Option B

    Both A and R are true but R is NOT the correct explanation of A

  • Option C

    Both A and R are true and R is the correct explanation of A

  • Option D

    A is false but R is true

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• MCQmediumMagnetic effect of currentMotion of Charged Particles in a Magnetic Field

  A positive particle initially has parallel velocity component v∥ along +B. A uniform electric field E is applied antiparallel to B. At what time does the helical pitch momentarily become zero?

  Options

  • Option A

    mv∥/(qE)

  • Option B

    qE/(mv∥)

  • Option C

    2mv∥/(qE)

  • Option D

    mE/(qv∥)

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• MCQmediumMagnetic effect of currentMotion of Charged Particles in a Magnetic Field

  A positive particle enters normally into a strip of uniform magnetic field of width d with speed v. The field is perpendicular to the plane of motion and the magnetic radius is r=mv/(qB). For d<r, what is the deflection angle φ before it crosses the far boundary?

  Options

  • Option A

    sin⁻¹(d/r)

  • Option B

    cos⁻¹(d/r)

  • Option C

    2sin⁻¹(d/r)

  • Option D

    π-sin⁻¹(d/r)

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• Multi-correctmediumMagnetic effect of currentMotion of Charged Particles in a Magnetic Field

  A charged particle follows a helical path in a uniform magnetic field. If B is doubled while its initial velocity components remain unchanged, which statements are correct?

  Select all that apply

  • Option A

    The helical radius halves.

  • Option B

    The cyclotron period halves.

  • Option C

    The pitch halves.

  • Option D

    The speed halves.

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