The magnetic induction of a uniform magnetic field changes according to the law B = (2 + 5t ^ 2) 10-2 T.

| August 1, 2021 | education

The magnetic induction of a uniform magnetic field changes according to the law B = (2 + 5t ^ 2) 10-2 T. Determine the dependence of the magnetic flux and EMF of induction on time, if the circuit with an area of S = 10 ^ -2 m2 is located perpendicular to the lines of magnetic induction. Determine the EMF of induction at the end of the fifth second

B (t) = (2 + 5 * t ^ 2) 10 ^ -2 T.

S = 10 ^ -2 m2.

∠β = 90 °.

t = 5 s.

Ф (t) -?

EMF (t) -?

The magnetic flux Ф is called a physical quantity equal to the product of the magnetic induction B by the area S, which it penetrates, and by the cosine of the angle between B and the perpendicular to the plane of the contour: Ф = B * S * cosα.

∠α = 90 ° – ∠β = 90 ° – 90 ° = 0 °, cos0 ° = 1.

F (t) = B (t) * S = (2 + 5 * t ^ 2) * 10-2 m2 * 10 ^ -2 T = (2 + 5 * t ^ 2) * 10-4 Vb.

Ф (5 s) = (2 + 5 * (5 s) ^ 2) * 10 ^ -4 Vb = 127 * 10 ^ -4 Vb.

EMF (t) = Ф (t) “= ((2 + 5 * t ^ 2) 10 ^ -2 T)” = 5 * 10 ^ -2 * 2 * t = 10 * t * 10 ^ -2 V.

EMF (5 s) = 50 * 10 ^ -2 V = 0.5 V.

Answer: F (t) = (2 + 5 * t ^ 2) * 10 ^ -4 Wb, F (5 s) = 127 * 10 ^ -4 Wb, EMF (t) = 10 * t * 10 ^ -2 V, EMF (5 s) = 0.5 V.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.