Chapter 30: Q. 45 (page 871)

A $2.0 c m \times 2.0 c m$ square loop of wire with resistance $0.010 Ω$ has one edge parallel to a long straight wire. The near edge of the loop is cm from the wire. The current in the wire is increasing at the rate of $100 A / s$ . What is the current in the loop?

Short Answer

Expert verified

The current in loop, $I_{induced} = 44.2 μ A$

Step by step solution

Introduction of loop

A loop is an electromagnetic system that uses two wires to send signals to a device. It can be used to produce energy or transmit data.

Simplify by values

Given values:

$A = 2.0 cm \times 2.0 cm$

$R = 0.010 Ω$ (ohm )

$d = 1.0 cm$

Magnetic flux of wire at distance :

$B = \frac{μ_{o} I}{2 π x}$

For a small strip of width $d x$ flux:

$d ϕ = d A B = \frac{μ_{o} I}{2 π x} (0.02 d x)$

$ϕ = \int_{0.01}^{0.03} \frac{μ_{o} I}{2 π x} d x = \frac{μ_{o} I}{2 π} \ln 3 (0.02)$

Find the worth of induce current

$ε = \frac{d ϕ}{d t} \cdot I_{induced} = \frac{ε}{R}$
$\Rightarrow I_{induced} = \frac{μ_{o}}{2 π R} \ln 3 \frac{d I}{d t} \times (0.02)$

localid="1650218054027">⇒Iinduced=4π×10×(1.098)m2π×0.1Ω×100×(0.02)

$\Rightarrow I_{induced} = 44.2 μ A$

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A $2.0 c m \times 2.0 c m$ square loop of wire with resistance $0.010 Ω$ has one edge parallel to a long straight wire. The near edge of the loop is cm from the wire. The current in the wire is increasing at the rate of $100 A / s$ . What is the current in the loop?

Short Answer

Step by step solution

Introduction of loop

Simplify by values

Find the worth of induce current

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A 2.0cm×2.0cmsquare loop of wire with resistance0.010Ωhas one edge parallel to a long straight wire. The near edge of the loop is cm from the wire. The current in the wire is increasing at the rate of 100A/s. What is the current in the loop?

Short Answer

Step by step solution

Introduction of loop

Simplify by values

Find the worth of induce current

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fluids

Wave Optics

Fields in Physics

Oscillations

Geometrical and Physical Optics

Solid State Physics

Study anywhere. Anytime. Across all devices.

A $2.0 c m \times 2.0 c m$ square loop of wire with resistance $0.010 Ω$ has one edge parallel to a long straight wire. The near edge of the loop is cm from the wire. The current in the wire is increasing at the rate of $100 A / s$ . What is the current in the loop?