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.

Explanation:

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

where:

variation of the magnetic flux

is the variation of time

#The magnetic flux through the coil is expressed as:

Where:

N- number of circular loops

A-is the Area of each loop()

B-is the magnetic strength of the field.

- is the angle between the direction of the magnetic field and the normal to the area of the coil.

=0.0250T/s is given as rate at which the magnetic field increases.

#Substitute in the emf equation:

Hence, the induced emf is

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