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21 June, 07:34

A proton (mass = 1.67*10-27 kg, charge = 1.6*10-19 C) travelling with speed 1*106 m/s enters a region of space containing a uniform magnetic field of 1.2 T. What is the time t required for the proton to re-emerge into the field-free region? t =

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  1. 21 June, 07:47
    0
    The time taken will be 2.73*10^ (-8) sec

    Explanation:

    After the proton enters in to a magnetic field, it follows circular motion in a clockwise direction.

    Proton will re-emerge into the field free region, when it has completed semi circle.

    Let the time required be t sec

    Force = qv*B

    centripetal force = mv^2/r

    Now taking both the equations

    r = mv / qB = 8.7*10^ (-3) m

    Total distance traveled will be = pi*r

    And, total time taken will be t = pi*r / v = 2.73*10^ (-8) sec
  2. 21 June, 10:19
    0
    The time required for the proton to re-emerge into the field-free region is 5.47 x 10⁻⁸ s

    Explanation:

    given;

    mass of proton, m = 1.67 * 10⁻²⁷ kg

    charge of proton, q = 1.6 * 10⁻¹⁹ C

    speed of proton, v = 1 * 10⁶ m/s

    uniform magnetic field, B = 1.2 T

    Force on the proton due to uniform magnetic field = qvB

    Force on the proton in the circular region = ma = mv²/r

    The time required for the proton to re-emerge into the field-free region, is the same as the time required for the proton to return to its starting position. During this period, the proton has made one complete revolution.

    v = 2πr/t

    t = 2πr/v

    where;

    t is the required for the proton to re-emerge into the field-free region

    r is the radius of the circular region

    mv²/r = qvB

    r = mv²/qvB

    r = mv/qB

    r = (1.67 * 10⁻²⁷ x 1 * 10⁶) / (1.6 * 10⁻¹⁹ x 1.2)

    r = 8.698 x 10⁻³ m

    t = 2πr/v

    t = (2π x 8.698 x 10⁻³) / (1 * 10⁶)

    t = 5.47 x 10⁻⁸ s

    Therefore, the time required for the proton to re-emerge into the field-free region is 5.47 x 10⁻⁸ s
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