The positron has the same mass as an electron, with an electric charge of +e. A positron follows a uniform circular motion of radius 5.03 mm

Question

The positron has the same mass as an electron, with an electric charge of +e. A positron follows a uniform circular motion of radius 5.03 mm due to the force of a uniform magnetic field of 0.85 T. How many complete revolutions does the positron perform If it spends 2.30 s inside the field? (electron mass = 9.11 x 10-31 kg, electron charge = -1.6 x 10-19 C)

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Yến Oanh 5 years 2021-08-06T12:26:06+00:00 1 Answers 31 views 0

Answers ( )

  1. thnahdat
    0
    2021-08-06T12:27:43+00:00
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    Answer:

    5.465 × 10^10 revolutions

    Explanation:

    Formula for Magnetic Field = m. v/ q . r

    M = mass of electron = mass of positron = 9.11 x 10^-31 kg,

    radius of the positron = 5.03 mm

    We convert to meters.

    1000mm = 1m

    5.03mm = xm

    Cross multiply

    x = 5.03/1000mm

    x = 0.00503m

    q = Electric charge = -1.6 x 10^-19 C

    Magnetic field (B) = 0.85 T

    Speed of the positron is unknown

    0.85 = 9.11 x 10^-31 kg × v/ -1.6 x 10^-19 C × 0.00503

    0.85 × 1.6 x 10^-19 C × 0.00503 = 9.11 x 10^-31 kg × v

    v = 0.85 × -1.6 x 10^-19 C × 0.00503/9.11 x 10^-31 kg

    v = 6.8408 ×10-22/ 9.11 x 10^-31 kg

    v = 750911086.72m/s

    Formula for complete revolutions =

    Speed × time / Circumference

    Time = 2.30s

    Circumference of the circular path = 2πr

    r =0.00503

    Circumference = 2 × π × 0.00503

    = 0.0316044221

    Revolution = 750911086.72 × 2.30/0.0316044221

    = 1727095499.5/0.0316044221

    = 546541562294 revolutions

    Approximately = 5.465 × 10^10 revolutions

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