A very long, straight solenoid with a cross-sectional area of 2.37 cm^2 is wound

Question

A very long, straight solenoid with a cross-sectional area of 2.37 cm^2 is wound with 87 turns of wire per centimeter. Starting at t = 0, the current in the solenoid is increasing according to i(t) = (0.178 A/s^2)t^2. A secondary winding of 5 turns encircles the solenoid at its center, such that the secondary winding has the same cross-sectional area as the solenoid. What is the magnitude of the emf induced in the secondary winding at the instant that the current in the solenoid is 3.2 A ? Express your answer with the appropriate units.

Explanation / Answer

E= -d(phi)/dt

N x phi = B x A

B= (mu)ni

dB/dt= (mu)n di/dt

E= -NA (mu)n di/dt

di/dt= 0.178 x 2 x t

E=  -NA (mu)n 0.178 x 2 x t

Putting values,

When current is 3.20 A, t= 4.242s approx.

5 x 2.37 x 10^-4 x 4 x 3.14 x 10^-7 x 87 x 10^2 x 0.178 x 2 x 4.242 = 19554.553x 10^-9 V

= 0.195 x 10^-4 V

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.