Problem 29.49 Part A A very long, straight solenoid with a cross-sectional area

Question

Problem 29.49 Part A A very long, straight solenoid with a cross-sectional area of 1.86 cm4 is wound with 90.3 turns of wire per centimeter. Starting at t-0, the current in the solenoid is increasing according to i(t) (0.165 A/s2 )t2. 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. Submit My Answers Give Up Incorrect; Try Again; 5 attempts remaining

Explanation / Answer

A) n = 90.3 turns/cm = 9030 turns/metre

The field inside the long solenoid is given by B = ni
B = 4x10 x 9030 x 0.165t² = 1.87x10³ t²

dB/dt = 3.74x10³ t
________________________________

A = 1.86cm² = 1.86x10 m²

|Emf| = rate of change of flux linkage

|Emf| = d(NAB)/dt = NA dB/dt
= 5 x 1.86x10 x 3.74x10³ t
= 3.48x10 t
_______________________________

If T is the time at which the current = 3.2A
3.2 = 0.165T²
T = 4.4s
_________________________________

|emf| = 3.48x10 T
= 3.48 x x10 x4.4
= 1.53x10 V

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

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