A circular loop of wire with radius 2.00 cm and resistance 0.600 Ω is in a region of a spatially uniform magnetic field B⃗ that is perpendic

Question

A circular loop of wire with radius 2.00 cm and resistance 0.600 Ω is in a region of a spatially uniform magnetic field B⃗ that is perpendicular to the plane of the loop. At t = 0 the magnetic field has magnitude B0=3.00T. The magnetic field then decreases according to the equation B(t)=B0e−t/τ, where τ=0.500s.

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Minh Khuê 3 years 2021-08-20T00:37:18+00:00 1 Answers 0 views 0

Answers ( )

  1. quangkhai
    0
    2021-08-20T00:38:38+00:00
    Reply

    Answer:

    Incomplete questions

    Let assume we are asked to find

    Calculate the induced emf in the coil at any time, let say t=2

    And induced current

    Explanation:

    Flux is given as

    Φ=NAB

    Where

    N is number of turn, N=1

    A=area=πr²

    Since r=2cm=0.02

    A=π(0.02)²=0.001257m²

    B=magnetic field

    B(t)=Bo•e−t/τ,

    Where Bo=3T

    τ=0.5s

    B(t)=3e(−t/0.5)

    B(t)=3exp(-2t)

    Therefore

    Φ=NAB

    Φ=0.001257×3•exp(-2t)

    Φ=0.00377exp(-2t)

    Now,

    Induce emf is given as

    E= – dΦ/dt

    E= – 0.00377×-2 exp(-2t)

    E=0.00754exp(-2t)

    At t=2

    E=0.00754exp(-4)

    E=0.000138V

    E=0.138mV

    b. Induce current

    From ohms laws

    V=iR

    Given that R=0.6Ω

    i=V/R

    i=0.000138/0.6

    i=0.00023A

    i=0.23mA

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