Chapter 30: Q. 46 (page 872)

FIGURE shows a $4.0$ -cm-diameter loop with resistance $0.10 Ω$ around a $2.0$ -cm-diameter solenoid. The solenoid is $10$ cm long, has $100$ turns, and carries the current shown in the graph. A positive current is $c w$ when seen from the left. Find the current in the loop at $(a) t = 0.5 s, (b) t = 1.5 s, a n d (c) t = 2.5 s .$

Short Answer

Expert verified

(a) By assign, $t = 0.5 \to I_{induced} = 0 A$

(b) By assign, $t = 1.5 \to I_{induced} = 12.56 \times 10^{- 5} A$

Step by step solution

Introduction

Given values:

$R = 0.1 Ω$

$n = 1000$

$r = R^{'} = 2 \times 10^{- 2} m$

$r = 1 \times 10^{- 2}$

$B_{s} = μ_{o} n I$

Use next equations,

$E (2 π R) = π r^{2} \frac{d B}{d t}$

$E (2 π R^{'}) = π r^{2} μ_{o} n \frac{d I}{d t}$

$E = \frac{π r^{2}}{2 π R^{'}} μ_{o} n \frac{d I}{d t}$

$E = \frac{r^{2} μ_{o} n}{2 R^{'}} \frac{d I}{d t}$

$I_{induced} = \frac{{(10^{- 2})}^{2}}{2 \times 2 \times 10^{- 2}} \times (4 π \times 10^{- 7}) \times 1000 \frac{d I}{d t} = 3.14 \times 10^{- 6} \frac{d I}{d t}$

Find Iinduced

a.) $I_{induced}$ at $t = 0.5$ :

$I_{induced} = 3.14 \times 10^{- 6} \times 0$

$I_{induced} = 0 A \to |\frac{d I}{d t} = 0|$

b.) $I_{induced}$ at $t = 1.5$ :

$I_{induced} = 3.14 \times 10^{- 6} \times 40$

$I_{induced} = 12.56 \times 10^{- 5} A \to |\frac{d I}{d t} = 40|$

c.) $I_{induced}$ at $t = 2.5$ :

$I_{induced} = 0 A \to |\frac{d I}{d t} = 0|$

Explain with graph

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Short Answer

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Find Iinduced

Explain with graph

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FIGURE shows a 4.0-cm-diameter loop with resistance 0.10Ωaround a 2.0-cm-diameter solenoid. The solenoid is 10 cm long, has 100turns, and carries the current shown in the graph. A positive current is cwwhen seen from the left. Find the current in the loop at(a)t=0.5s,(b)t=1.5s,and(c)t=2.5s.

Short Answer

Step by step solution

Introduction

Find Iinduced

Explain with graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Force

Electrostatics

Fluids

Mechanics and Materials

Fields in Physics

Kinematics Physics

Study anywhere. Anytime. Across all devices.