Two long, parallel wires separated by 5.0 mm each carry a current of 60 A. These two currents are oppositely directed. What is the magnitude

Question

Two long, parallel wires separated by 5.0 mm each carry a current of 60 A. These two currents are oppositely directed. What is the magnitude of the magnetic field at a point that is between the two wires and 2.0 mm from one of the two wires

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Khải Quang 5 months 2021-08-28T08:59:40+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-28T09:00:53+00:00

    Answer:

    0.002T

    Explanation:

    It is given that,

    Distance between two parallel wires, d = 5 mm = 0.005

    Current in each wire, I = 60 A

    Let B is the magnitude of the magnetic field at a point that is between the two wires and 2.0 mm from one of the two wires.

    calculating the magnetic field due to first wire is given by :

    B_1=\dfrac{\mu_oI}{2\pi d}B_1=\dfrac{4\pi \times 10^{-7}\times 60}{2\pi \times 0.002}  B_1=0.006\ T

    The magnetic field due to second wire is given by :

    B_2=\dfrac{\mu_oI}{2\pi d}\\B_2=\dfrac{4\pi \times 10^{-7}\times 60}{2\pi \times 0.003}  \\B_2=0.004\ T

    Let B is the net magnetic field from wire A, so,

    ,B=B_1-B_2B=0.006-0.004B = 0.002 T

    0
    2021-08-28T09:01:04+00:00

    Given Information:  

    Distance between wires = d = 5 mm = 0.005 m

    Current in wires = I = 60 A

    Required Information:  

    Magnetic field at distance 2 mm between two wires  = B = ?  

    Answer:  

    B = 0.010 T

    Explanation:  

    When two parallel wires carrying a current I are separated by a distance d then the magnetic field is given by

    B1 = μ₀I/2πd1

    B2 = μ₀I/2πd2

    Where μ₀= 4πx10⁻⁷ is the permeability of free space

    The overall magnitude of magnetic field is

    B = B1 + B2

    Since the two wires are separated by 0.005 m then

    d1 = 0.005 – 0.002 = 0.003 m

    d2 = 0.002 m

    B1 = 4πx10⁻⁷*60/2π*0.003

    B1 = 0.004 T

    B2 = 4πx10⁻⁷*60/2π*0.002

    B2 = 0.006 T

    B = 0.004 + 0.006

    B = 0.010 T

    Therefore, the magnitude of the magnetic field at a point between two wires and 0.002 m away from one of wire is 0.010 T

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