Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a I = 10 sin ( t )A , where = 1000 rad/s . A circular conducting loop (B) of radius 1 cm coaxially slides through the

Question

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a $I = 10 \sin (ω t) A, where ω = 1000 rad/s .$ A circular conducting loop (B) of radius 1 cm coaxially slides through the solenoid at speed v = 1 cm/s. The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is $\frac{α}{\sqrt{2}} μ A$ . The value of $α$ is ______.

[Resistance of the loop = $10 Ω$ ] [2026]

Smart Achievers · Accepted Answer

(3)

$EMF induced ε = A \frac{d B}{d t} = A μ_{0} n \frac{d i}{d t}$

$ε = A μ_{0} n i_{0} ω \cos ω t$

$current induced i = \frac{ε}{R} = \frac{π r^{2} μ_{0} n i_{0} ω}{R} \cos ω t$

$So i = \frac{π r^{2} μ_{0} n i_{0} ω}{\sqrt{2} R}$

$= \frac{π \times 10^{- 4} \times 4 π \times 10^{- 7} \times 500 \times 10 \times 10^{3}}{\sqrt{2} \times 10}$

$= \frac{20 π^{2}}{\sqrt{2}} \times 10^{- 6}$

$= \frac{197}{\sqrt{2}} μ A$

Solution

1 280

2 80

3 197

4 100

Want Us to Email you About Special Offers & Updates?