Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

Answers without the blur.

Just sign up for free and you're in.

Short Answer

In Figure, a wire loop of lengths L = 40.0 cm and W = 25.0 cm lies in a magnetic field $\vec{B}$ .(a)What is the magnitude $ε$ if $\vec{B} = (4.00 \times 10^{- 2} \frac{T}{m}) y \hat{k}$ ?(b)What is the direction (clockwise or counterclockwise—or “none” if 0) of the emf induced in the loop if $\vec{B} = (4.00 \times 10^{- 2} \frac{T}{m}) y \hat{k}$ ?(c)What is the $ε$ if $\vec{B} = (6.00 \times 10^{- 2} \frac{T}{s}) t \hat{k}$ (d)what is the direction if $\vec{B} = (6.00 \times 10^{- 2} \frac{T}{s}) t \hat{k}$ (e)What is the $ε$ if $\vec{B} = (8.00 \times 10^{- 2} \frac{T}{m . s}) y t \hat{k}$ (f)What is the direction if $\vec{B} = (6.00 \times 10^{- 2} \frac{T}{s}) t \hat{k}$ (g)What is the $ε$ if $\vec{B} = (3.00 \times 10^{- 2} \frac{T}{m . s}) x t \hat{k}$ (h)What is the direction if $\vec{B} = (3.00 \times 10^{- 2} \frac{T}{m . s}) x t \hat{k}$ (i)What is the if $\vec{B} = (5.00 \times 10^{- 2} \frac{T}{m . s}) y t \hat{k}$ (j)What is the direction if $\vec{B} = (5.00 \times 10^{- 2} \frac{T}{m . s}) y t \hat{k}$

Magnitude of emf induced $ε = 0$ .
Direction of the emf is none.
Magnitude of emf induced $ε = 6 mV$ .
Direction of the emf is clockwise.
Magnitude of emf induced $ε = 1 mV$ .
Direction of the emf is clockwise.
Magnitude of emf induced $ε = 0$ .
Direction of the emf is none.
Magnitude of emf induced $ε = 0$ .
Direction of the emf is none.

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Given

Length of loop, L = 40 cm = 0.4 m
Width of the loop, w = 25.0 cm=0.25 m

Step 2: Determining the concept

By using the concept of the magnetic flux, Faraday’s law and Lenz’s law, find the magnitude and the direction of the induced emf in all the cases.

Faraday's law of electromagnetic induction states, Whenever a conductor is

placed in a varying magnetic field, an electromotive force is induced in it.

Lenz's law states that the current induced in a circuit due to a change in a magnetic field is directed to oppose the change in flux and to exert a mechanical force which opposes the motion.

Formulae are as follow:

Faraday's law $ε = \frac{d φ}{d t}$
Magnetic flux $φ = ϕ B d A$

Where, 𝜀 is emf, dt is time, $Φ$ is magnetic flux, B is magnetic field, A is area.

Step 3: (a) Determining the magnitude of emf induced ε

The magnetic flux passing through the coil is given by,

$φ = ϕ B . d A = ϕ B d A \cos θ φ = B A \cos θ$

The emf induced in coil is given by,

$ε = - \frac{d φ}{d t} ε = - \frac{d}{d t} [B A \cos θ] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1) ε = B A \sin θ$

Now, for the rectangular coil,

$A = 0.4 \times 0.25 A = 0.1 m^{2} ∴ ε = 0.1 B sinθ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2)$

For $B = 4 \times 10^{- 2} T / m) y \hat{k}$

As the unit vector $\hat{k}$ , it is along z axis and it is perpendicular to the coil. But it is not changing with time. Hence, from equation 1,

$ε = - \frac{d}{d t} [B A \cos θ] ε = 0$

Hence, the emf induced in the coil is zero.

Step 4: (b) Determining the direction of the emf, (clockwise or anticlockwise or none.)

From a),

Hence, the direction of the emf is none.

Step 5: (c) Determining the magnitude of emf induced

For $B = 6 \times 10^{- 2} T / s) t \hat{k}$

It is perpendicular to the coil and changes with time. From equation 2,

$ε = 0.1 Bsinθ ε = 0.1 \times 6 \times 10^{- 2} \sin 90 ε = 0.1 \times 6 \times 10^{- 2} \times 1 ε = 0.1 \times 6 \times 10^{- 2} V ε = 6 \times 10^{- 3} V ε = 6 mV$

Hence, emf induced in the loop will be 6 mV.

Step 6: (d) Determining the direction of the emf, (clockwise or anticlockwise or none.)

Since, the magnetic field is directed into the page,

Hence, the direction of the induced emf is clockwise.

Step 7: (e) Determining the magnitude of emf induced ε

For $B = 8 \times 10^{- 2} T / m . s) yt \hat{k}$ ,

which is in the direction of y axis, that is, along the width of the coil.

$φ = ϕ B . d A φ = ϕ 8 \times 10^{- 2} y t \times d (l \times w)$

w is along x axis.

$φ = l \times 8 \times 10^{- 2} t \int_{0}^{W} y d y φ = 0.4 \times 8 \times 10^{- 2} t \times \frac{w^{2}}{2}$

$φ = 0.4 \times 8 \times 10^{- 2} \times t \times \frac{{(0.25)}^{2}}{2} φ = 0.1 t \times 10^{- 2}$

The emf induced can be calculated as,

$ε = \frac{dφ}{dt} ε = \frac{d}{dt} [0.1 t \times 10^{- 2}] ε = 1 \times 10^{- 3} V ε = 1 mV$

Hence, the emf induced in the coil is 1 mV.

Step 8: (f) Determining the direction of the emf, (clockwise or anticlockwise or none.)

From e),

Hence, the direction of the induced emf will be clockwise.

Step 9: (g) Determining the magnitude of emf induced ε

For $B = 3 \times 10^{- 2} T / m . s) xt \hat{j}$ , the magnetic field is directed along the y axis i.e. parallel to the coil.

The flux through the coil i.e. $φ = 0$

$ε = 0$

Hence, the emf induced in the coil is zero.

Step 10: (h) Determining the direction of the emf, (clockwise or anticlockwise or none.)

From g),

Hence, the direction of emf will be none.

Step 11: (i) Determining the magnitude of emf induced ε

For $B = 5 \times 10^{- 2} T / m . s) yt \hat{i}$ , the magnetic field is directed along the x axis i.e. parallel to the coil.

The flux through the coil i.e. $φ = 0$

$ε = 0$

Hence, the emf induced in the coil is zero.

Step 12: (j) Determining the direction of the emf, (clockwise or anticlockwise or none.)

From i),

Hence, the direction of emf will be none.

Therefore, by using the concept of the magnetic flux, Faraday’s law and Lenz’s law, find the magnitude and the direction of the induced emf in all the cases.

Find Study Materials for

Create Study Materials

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given

Step 2: Determining the concept

Step 3: (a) Determining the magnitude of emf induced ε

Step 4: (b) Determining the direction of the emf, (clockwise or anticlockwise or none.)

Step 5: (c) Determining the magnitude of emf induced

Step 6: (d) Determining the direction of the emf, (clockwise or anticlockwise or none.)

Step 7: (e) Determining the magnitude of emf induced ε

Step 8: (f) Determining the direction of the emf, (clockwise or anticlockwise or none.)

Step 9: (g) Determining the magnitude of emf induced ε

Step 10: (h) Determining the direction of the emf, (clockwise or anticlockwise or none.)

Step 11: (i) Determining the magnitude of emf induced ε

Step 12: (j) Determining the direction of the emf, (clockwise or anticlockwise or none.)

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Select your language

Fundamentals Of Physics

Answers without the blur.

Short Answer

Step by Step Solution

Step 1: Given

Step 2: Determining the concept

Step 3: (a) Determining the magnitude of emf induced ε

Step 4: (b) Determining the direction of the emf, (clockwise or anticlockwise or none.)

Step 5: (c) Determining the magnitude of emf induced

Step 6: (d) Determining the direction of the emf, (clockwise or anticlockwise or none.)

Step 7: (e) Determining the magnitude of emf induced ε

Step 8: (f) Determining the direction of the emf, (clockwise or anticlockwise or none.)

Step 9: (g) Determining the magnitude of emf induced ε

Step 10: (h) Determining the direction of the emf, (clockwise or anticlockwise or none.)

Step 11: (i) Determining the magnitude of emf induced ε

Step 12: (j) Determining the direction of the emf, (clockwise or anticlockwise or none.)

Most popular questions for Physics Textbooks

Want to see more solutions like these?

Recommended explanations on Physics Textbooks

Work Energy and Power

Radiation

Astrophysics

Physics of Motion

Scientific Method Physics

Fluids

Torque and Rotational Motion

Nuclear Physics

Fields in Physics

Measurements

Space Physics

Electricity

Physical Quantities and Units

Medical Physics

Electrostatics

Further Mechanics and Thermal Physics

Mechanics and Materials

Engineering Physics

Energy Physics

Force

Particle Model of Matter

Waves Physics

Magnetism

Modern Physics

Atoms and Radioactivity

Dynamics

Electricity and Magnetism

Conservation of Energy and Momentum

Fundamentals of Physics

Kinematics Physics

Circular Motion and Gravitation

Linear Momentum

Rotational Dynamics

Oscillations

Translational Dynamics

Geometrical and Physical Optics

Thermodynamics

Magnetism and Electromagnetic Induction

Electromagnetism

Electric Charge Field and Potential

Turning Points in Physics