Physics of Everyday Phenomena
Physics of Everyday Phenomena
9th Edition
ISBN: 9781259894008
Author: W. Thomas Griffith, Juliet Brosing Professor
Publisher: McGraw-Hill Education
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Chapter 14, Problem 3SP

A rectangular coil of wire has dimensions of 4 cm by 8 cm and is wound with 70 turns of wire. It is turned between the pole faces of a horseshoe magnet that produces an approximately uniform field of 0.5 T, so that sometimes the plane of the coil is perpendicular to the field and sometimes it is parallel to the field.

a.    What is the area bounded by the rectangular coil?

b.    What is the maximum value of the total magnetic flux that passes through the coil as it is turned?

c.    What is the minimum value of the total flux through the coil as it turns?

d.    If the coil makes one complete turn each second and turns at a uniform rate, what is the time involved in changing the flux from the maximum value to the minimum value?

e.    What is the average value of the voltage generated in the coil as it passes from the maximum to the minimum value of flux?

(a)

Expert Solution
Check Mark
To determine

The area bounded by the rectangular coil.

Answer to Problem 3SP

The area of coil is 32cm2.

Explanation of Solution

Given Info Dimensions of rectangular coil is 4 cm by 8 cm, number of turns in coil is 70 and the magnetic field is 0.5T.

Write the formula to calculate the area of coil.

A=lb

Here,

A is the area of coil

l is the length of coil

b is the breadth of coil

Substitute 8 cm for l and 4 cm for b in the above equation to find A.

A=(8 cm)(4 cm)=32cm2

Conclusion:

Therefore, the area of coil is 32cm2.

(b)

Expert Solution
Check Mark
To determine

The maximum value of magnetic flux through coil.

Answer to Problem 3SP

The maximum value of magnetic flux is 0.112Tm2.

Explanation of Solution

Given Info Dimensions of rectangular coil is 4 cm by 8 cm, number of turns in coil is 70 and the magnetic field is 0.5T.

Magnetic flux through the coil is maximum when the plane of coil is perpendicular to the magnetic field lines.

Write the formula to calculate the magnetic flux.

ϕ=NBAcosθ

Here,

ϕ is the magnetic flux

N is the number of turns

B is the magnetic field

θ is the angle between plane of coil and magnetic field lines

Substitute 70 for N,0.5T for B,32cm2 for A and 0° for θ in the above equation to find ϕmax.

ϕmax=(70)(0.5T)(32cm2(1m2104cm2))(cos0°)=0.112Tm2

Conclusion:

Therefore, the maximum value of magnetic flux is 0.112Tm2.

(b)

Expert Solution
Check Mark
To determine

The minimum value of magnetic flux through coil.

Answer to Problem 3SP

The minimum value of magnetic flux is 0.112Tm2.

Explanation of Solution

Given Info Dimensions of rectangular coil is 4 cm by 8 cm, number of turns in coil is 70 and the magnetic field is 0.5T.

Magnetic flux through the coil is minimum when the plane of coil is parallel to magnetic field lines.

Write the formula to calculate the magnetic flux.

ϕ=NBAcosθ

Substitute 70 for N,0.5T for B,32cm2 for A and 90° for θ in the above equation to find ϕmin.

ϕmin=(70)(0.5T)(32cm2(1m2104cm2))(cos90°)=0Tm2

Conclusion:

Therefore, the minimum value of magnetic flux is 0Tm2.

(d)

Expert Solution
Check Mark
To determine

The time required for change in flux.

Answer to Problem 3SP

The time required for flux change is 0.25s.

Explanation of Solution

Given Info: The current through the wires are 8A and 12A, separation between wires is 4cm and coil makes one complete turn in one second.

Field lines become perpendicular and parallel to plane of loop two times during one complete turn of coil. This means that during one complete turn, change in maximum value of flux to minimum occurs four times.

Write the formula to calculate the time required for flux change.

t=Tn

Here,

t is the time taken for flux change

T is the time taken by coil for one complete turn

n is the number of times which flux changes from maximum to minimum in one complete turn

Substitute 1s for T and 4 for n in the above equation to find t.

t=1s4=0.25s

Conclusion:

Therefore, time taken for flux change is 0.25s.

(e)

Expert Solution
Check Mark
To determine

The average value of induced voltage inn coil.

Answer to Problem 3SP

The average value of induced voltage is 0.448V.

Explanation of Solution

Write the Faraday’s law to calculate the average value of induced voltage.

ε=ϕmaxϕmint

Here,

ε is the average value of induced voltage

Substitute 0.112Tm2 for ϕmax,0Tm2 for ϕmin and 0.25s for t in the above equation to find ε.

ε=0.112Tm20Tm20.25s=0.448V

Conclusion:

Therefore, the average value of induced voltage is 0.448V.

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Chapter 14 Solutions

Physics of Everyday Phenomena

Ch. 14 - A uniform magnetic field is directed horizontally...Ch. 14 - A positively charged particle is momentarily at...Ch. 14 - If a uniform magnetic field is directed...Ch. 14 - Why does the magnetic force on a current-carrying...Ch. 14 - If we look down at the top of a circular loop of...Ch. 14 - If we were to represent the current loop of...Ch. 14 - A current-carrying rectangular loop of wire is...Ch. 14 - If the rectangular loop of wire shown in question...Ch. 14 - Because the magnetic fields of a coil of wire and...Ch. 14 - In what respect is a simple ammeter designed to...Ch. 14 - Does an ac motor require a split-ring commutator...Ch. 14 - Which type of motor typically runs at a fixed...Ch. 14 - If Faraday wound enough turns of wire on the...Ch. 14 - Is a magnetic flux the same as a magnetic field?...Ch. 14 - A horizontal loop of wire has a magnetic field...Ch. 14 - Suppose the magnetic flux through a coil of wire...Ch. 14 - Two coils of wire are identical except that coil....Ch. 14 - Do the sensors that detect vehicles at stoplights...Ch. 14 - Under which conditions are inductive detectors...Ch. 14 - If the magnetic field produced by the magnets in a...Ch. 14 - Does a simple generator produce a steady direct...Ch. 14 - A simple generator and a simple electric motor...Ch. 14 - Can a transformer be used, as shown in the...Ch. 14 - By stepping up the voltage of an...Ch. 14 - Prob. 1ECh. 14 - Two long parallel wires, each carrying a current...Ch. 14 - Prob. 3ECh. 14 - Prob. 4ECh. 14 - A wire carries a current of 12 A. How much charge...Ch. 14 - A particle with a charge of 0.6 C is moving at...Ch. 14 - A straight segment of wire has a length of 12 cm...Ch. 14 - The magnetic force on a 60-cm straight segment of...Ch. 14 - A coil of wire with 150 turns has a...Ch. 14 - A loop of wire enclosing an area of 0.04 m2 has a...Ch. 14 - The magnetic flux through a coil of wire changes...Ch. 14 - A coil of wire with 120 turns and a...Ch. 14 - Prob. 13ECh. 14 - If 15 A of current are supplied to the primary...Ch. 14 - Prob. 15ECh. 14 - Prob. 16ECh. 14 - Two long parallel wires carry currents of 8 A and...Ch. 14 - A small metal ball with a charge of +0.08 C and a...Ch. 14 - A rectangular coil of wire has dimensions of 4 cm...Ch. 14 - Prob. 4SP
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