Question

The radius of curvature of the path of a charged particle in a uniform magnetic field is directly proportional toA) the particle’s charge.B) the particle’s momentum.C) the particle’s energy.D) the flux density of the field.E)All of these are correct

Answers

  1. Answer:

    B) the particle’s momentum.

    Explanation:

    We know that

    The centripetal force  on the particle when its moving in the radius R and velocity V

    F_c=\dfrac{m\times V^2}{R}

    The magnetic force on the particle when the its moving with velocity V in the magnetic filed B and having charge q

    F_m=q\times V\times B

    At the equilibrium condition

    F_m=F_c

    q\times V\times B=\dfrac{m\times V^2}{R}

    R=\dfrac{m\times V}{q\times B}

    Momentum = m V

    Therefore we can say that the radius of curvature is directly proportional to the particle momentum.

    B) the particle’s momentum.

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