A 514 turn solenoid , 21 cm long has a diameter of 2.6 cm. A 14 turn coil is tightly wound around the center of the solenoid. If the current in the solenoid increases uniformly from 0.3 A to 2.79 A in 0.8 s, what will be the induced emf in the short coil during this time

Explanation:

no of turns per unit length n = 514 / .21 = 2447.62 per meter .

magnetic field in solenoid = μ₀ nI

= 4π x 10⁻⁷ x 2447.62 x I = 3.07 x 10⁻³ I  T

magnetic flux through the small coil = 14 x 3.07 x 10⁻³ x π x 1.3² x10⁻⁴ I

φ= 72.63 x 10⁻⁷ I  Web

emf induced in it

= dφ / dt = 72.63 x 10⁻⁷ dI / dt

= 72.63 x 10⁻⁷ x ( 2.79 - .3) / .8

= 226 x 10⁻⁷ V

= 22.6 x10⁻⁶ V

= 22.6 μ V .