A 24cm-diameter circular loop of wire has a resistance of 200 ohm . It initially

Question

A 24cm-diameter circular loop of wire has a resistance of 200 ohm . It initially in a 0.45T magnetic field, with its plane perpendicular to B rightarrow . but is removed from the field in 130ms . A coil with 170 turns, a radius of 5.0 cm. and a resistance of 12 ohm surrounds a solenoid with 300turns/cm and a radius of 4.7cm; see the figure. The current in the solenoid changes at a constant rate from 0 to 2.2A in 0.14s. Calculate the magnitude and direction of the induced current in the 170-turn coil. Express your answer using two significant figures. The current flows from right to left through the resistor. The current flows from left to right through the resistor.

Explanation / Answer

1)

Induced emf,V= B*A/t

where B = magnetic field = 0.45 T

A = area = pi*(d^2/4) = pi*(0.24^2/4) = 0.0452 m2

t = 130 ms = 0.13 s

So, V = 0.452*0.0452/0.13 = 0.157 V

So, Power, P = V^2/R = 0.157^2/200 = 1.23*10^-4 W

So, energy dissipated = P*t = 1.23*10^-4*0.13

= 1.6*10^-5 J <-------------answer

2)

Maximum Magnetic field inside the solenoid, B = u*n*I

where u = permittivity of air = 1.26*10^-6

n = 300 turns/cm = 30000 turns/m

So, B = 1.26*10^-6*30000*2.2 = 8.32*10^-2 T

So, Induced Emf, V = N*B*A/t = 170*(8.32*10^-2)*(pi*0.05^2)/0.14 = 0.793 V

So, induced current, I = V/R = 0.793/12 = 0.066 A <----------answer

3)

Current flows from left ot right in the resistor <---- Given by Lenz's Law

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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