## Electromagnetic Induction in a Rectangular Loop### Problem DescriptionA loop of wire in the shape of a rectangle with width \( w \) and length \( L \), alongside a long, straight wire carrying a current \( I \), lies on a tabletop as depicted in the figure below.### (a) Magnetic Flux DeterminationDetermine the magnetic flux \( \Phi_B \) through the loop due to the current \( I \). Use the variable expressions provided: \( \mu_0 \) is the permeability of free space.#### Formula:\[\Phi_B = \frac{\mu_0 I L}{2\pi} \ln \left( \frac{h + w}{h} \right)\]### (b) Induced EMF CalculationSuppose the current varies over time as \( I = a + bt \), where \( a \) and \( b \) are constants. Calculate the magnitude of the electromotive force (emf) induced in the loop. Given \( b = 12.0 \, \text{A/s} \), \( h = 1.00 \, \text{cm} \), \( w = 15.0 \, \text{cm} \), and \( L = 1.50 \, \text{m} \).#### Result:Calculated induced emf = \( 9.98 \times 10^{-5} \, \text{V} \)**Question:** How do you determine the induced emf using the flux equation from part (a)?

Answered: Image /qna-images/answer/bd055ee8-d00c-4095-b0c2-d3ffecf9f849.jpg

A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in the figure below. i (a) Determine the magnetic flux through the loop due to the current I. (Use any variable stated above along with the following as necessary: μ.) = HOIL 2π In W h+w h (b) Suppose the current is changing with time according to I = a + bt, where a and b are constants. Determine the magnitude of the emf (in V) that is induced in the loop if b = 12.0 A/s, h = 1.00 cm, w = 15.0 cm, and L = 1.50 m. 9.98e-05 X How do you determine the induced emf from your equation for the flux from part (a)? V

A loop of wire in the shape of a rectangle of width w and length L and a long, straight wire carrying a current I lie on a tabletop as shown in the figure below. i (a) Determine the magnetic flux through the loop due to the current I. (Use any variable stated above along with the following as necessary: μ.) = HOIL 2π In W h+w h (b) Suppose the current is changing with time according to I = a + bt, where a and b are constants. Determine the magnitude of the emf (in V) that is induced in the loop if b = 12.0 A/s, h = 1.00 cm, w = 15.0 cm, and L = 1.50 m. 9.98e-05 X How do you determine the induced emf from your equation for the flux from part (a)? V

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ISBN:9781305952300

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Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

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Concept explainers

Magnetic Field Of Coaxial Cable

The word coaxial means same axis. So for a long straight cable to be coaxial, it must have concentric cylindrical shaped conductor around it. Coaxial cable (popularly called ‘coax’) has various applications ranging from current conductors to radiofrequency signal transmitters. This cable has lower emission losses and provides protection from electromagnetic interference which allows signals with less power to transmit over longer distances.For example, currents produced in the pickup of a stereo turntable generally travel to the amplifier through a coaxial cable.The self-inductance of a coaxial cable is another important characteristic, because it influences the propagation of electrical signals in the cable.

Question

## Electromagnetic Induction in a Rectangular Loop

### Problem Description
A loop of wire in the shape of a rectangle with width \( w \) and length \( L \), alongside a long, straight wire carrying a current \( I \), lies on a tabletop as depicted in the figure below.

### (a) Magnetic Flux Determination

Determine the magnetic flux \( \Phi_B \) through the loop due to the current \( I \). Use the variable expressions provided: \( \mu_0 \) is the permeability of free space.

#### Formula:
\[
\Phi_B = \frac{\mu_0 I L}{2\pi} \ln \left( \frac{h + w}{h} \right)
\]

### (b) Induced EMF Calculation

Suppose the current varies over time as \( I = a + bt \), where \( a \) and \( b \) are constants. Calculate the magnitude of the electromotive force (emf) induced in the loop. Given \( b = 12.0 \, \text{A/s} \), \( h = 1.00 \, \text{cm} \), \( w = 15.0 \, \text{cm} \), and \( L = 1.50 \, \text{m} \).

#### Result:
Calculated induced emf = \( 9.98 \times 10^{-5} \, \text{V} \)

**Question:** How do you determine the induced emf using the flux equation from part (a)?

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