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19 days ago

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

ects. 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.

1 answer:

kicyunya [2.2K]19 days ago

4 0

Response:

$1.138\times 10^{-3}V$

Details:

Utilizing Faraday's Newmann Lenz law enables the assessment of the induced emf within the loop:

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

where:

$d\Phi-$ represents the change in magnetic flux

$dt-$ symbolizes the change over time.

#The magnetic flux linked to the coil can be represented as:

$\Phi=NBA \ Cos \theta$

Where:

N represents the number of loops.

A denotes the area for each loop ( $A=\pi r^2=\pi \times 5^2=78.5398$ ).

B indicates the strength of the magnetic field.

$\theta=15\textdegree$ represents the angle between the magnetic field direction and the normal to the loop's area.

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

$\frac{dB}{dt}-$ =0.0250T/s is indicated as the rate of magnetic field increase.

#Plugging in values into the emf equation:

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

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

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