To practice Problem-Solving Strategy 29.1: Faraday’s Law. A metal detector uses a changing magnetic field to detect metallic objects. Suppos

Question

To practice Problem-Solving Strategy 29.1: Faraday’s Law. A metal detector uses a changing magnetic field to detect metallic objects. Suppose a metal detector that generates a uniform magnetic field perpendicular to its surface is held stationary at an angle of 15.0∘∘ to the ground, while just below the surface there lies a silver bracelet consisting of 6 circular loops of radius 5.00 cmcm with the plane of the loops parallel to the ground. If the magnetic field increases at a constant rate of 0.0250 T/sT/s, what is the induced emf EEEMF? Take the magnetic flux through an area to be positive when B⃗ B→B_vec crosses the area from top to bottom.

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Ngọc Hoa 5 years 2021-08-12T21:04:01+00:00 1 Answers 248 views 0

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  1. Sapo1
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    2021-08-12T21:05:08+00:00
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    Answer:

    1.138\times 10^{-3}V

    Explanation:

    Apply Faraday’s Newmann Lenz law to determine the induced emf in the loop:

    \epsilon=\frac{d\phi}{dt}

    where:

    d\Phi-variation of the magnetic flux

    dt-is the variation of time

    #The magnetic flux through the coil is expressed as:

    \Phi=NBA \ Cos \theta

    Where:

    N- number of circular loops

    A-is the Area of each loop(A=\pi r^2=\pi \times 5^2=78.5398)

    B-is the magnetic strength of the field.

    \theta=15\textdegree– is the angle between the direction of the magnetic field and the normal to the area of the coil.

    \epsilon=-\frac{d(78.5398\times 10^{-3}NB \ Cos \theta)}{dt}\\\\=-(78.5398\times 10^{-3}N\ Cos \theta)}{\frac{dB}{dt}

    \frac{dB}{dt}-=0.0250T/s is given as rate at which the magnetic field increases.

    #Substitute in the emf equation:

    =-(78.5398\times 10^{-3} m^2 \times 6\ Cos 15 \textdegree)\times 0.0250T/s\\\\=1.138\times 10^{-3}V

    Hence, the induced emf is 1.138\times 10^{-3}V

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