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.

Answer 1

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