A coil with a diameter of 0.5 m, having 1000 turns, is in a decreasing magnetic field from 0.5 T to zero.

A coil with a diameter of 0.5 m, having 1000 turns, is in a decreasing magnetic field from 0.5 T to zero. The field change occurs in 1 s. Determine the induction EMF arising in the coil if the plane of the turns is perpendicular to the lines of force. Take into account that the cross-sectional area is S = пr2.

Induction EMF formula:
E = -N * F / t
E = -N * Ф ‘* (formula using derivative)
Hence the change in magnetic flux:
Ф = BScos (B, n)
where n is the normal (vector perpendicular to the plane of the area S)
Since the plane of the turns is perpendicular to the lines of force, the cosine will be equal to 1:
Ф = BS
Coil cross-section:
S = pi * r ^ 2
S = pi * d ^ 2/4
Let’s substitute:
E = -N * F / t
E = -N * (B1 – B2) * S / t
Since the change in induction goes from 0.5 T to 0, the difference between the values ​​of induction in 1 and 2 cases will be equal to 0.
E = – N * B2 * pi * d ^ 2 / 4t
E = – 1000 * 0.5 * 3.14 * 0.5 * 0.5 ^ 2/4 * 1
E = – 49.0625 = – 49.1 (B)
Since the magnetic field has decreased, the EMF will be negative.
Answer: E = – 49.1 (B)