Ametal 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 cm with the plane of the loops parallel to the ground. if the magnetic field increases at a constant rate of 0.0250 t/s, what is the induced emf e? take the magnetic flux through an area to be positive when b⃗ crosses the area from top to bottom.

Explanation:

The induced emf in the loop is given by Faraday's Newmann Lenz law:

(1)

where

is the variation of magnetic flux

is the variation of time

The magnetic flux through the coil is given by

(2)

where

N = 6 is the number of loops

A is the area of each loop

B is the magnetic field strength

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

Since the radius of each loop is r = 5.00 cm = 0.05 m, the area is

Substituting (2) into (1), we find

where

is the rate of variation of the magnetic field

Substituting numbers into the last formula, we find

Induced emf,

Explanation:

It is given that,

Number of circular loop, N = 6

A uniform magnetic field perpendicular to its surface is held stationary at an angle of 15 degrees to the ground.

Radius of the loop, r = 5 cm = 0.05 m

Change in magnetic field,

Due to the change in magnetic field, an emf will be induced. Let E is the induced emf in the coil. it is given by :

= magnetic flux

So, the induced emf in the loop is . Hence, this is the required solution.

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