General Physics, 2nd Edition
General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Question
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Chapter 20, Problem 39E

(a)

To determine

The magnetic field inside the solenoid.

(a)

Expert Solution
Check Mark

Answer to Problem 39E

The magnetic field inside the solenoid is 4πkmknI.

Explanation of Solution

Write the expression for Ampere’s law.

    Bdl=4πkNI        (1)

Here, B is the magnetic field, dl is small elemental length, k is constant, n is the number of and I is the current.

Conclusion:

The magnetic field and the length of the solenoid is parallel to each other.

Rewrite equation (1).

    Bdl=4πkkmNI

Here, km is the magnetic constant for coil.

Substitute l for the closed integral and (nl) for N in the above equation.

    B(l)=4πkmk(nl)IB=4πkmknI

Here, l is the length of the rectangle and n is the number of turns per unit length.

Thus, the magnetic field inside the solenoid is 4πkmknI.

(b)

To determine

The amount of energy stored per unit volume in the solenoid.

(b)

Expert Solution
Check Mark

Answer to Problem 39E

The energy stored per unit volume of the solenoid is 2πN2kmkI2l2.

Explanation of Solution

Write the expression for magnetic field inside the solenoid.

    B=4πkmknI

Write the expression for the magnitude of the inductance.

    L=NϕI

Here, L is the inductance and ϕ is the induced magnetic flux.

Substitute (BA) for ϕ in the above expression.

    L=N(BA)I        (2)

Here, A is the area of the solenoid.

Write the expression of magnetic field per unit volume of the solenoid.

    U=12AlLI2        (3)

Here, U is the energy per unit volume.

Conclusion:

Substitute 4πkmknI for B in equation (2).

    L=N(4πkmknI)AI=4πNkmknA

Substitute 4πNkmknA for L in equation (3).

    U=12Al(4πNkmknA)I2=2πNkmknI2l

Substitute (Nl) for n in the above equation.

    U=2πN2kmkI2l2

Thus, the energy stored per unit volume of the solenoid is 2πN2kmkI2l2.

(c)

To determine

The value of a constant..

(c)

Expert Solution
Check Mark

Answer to Problem 39E

The value of the constant is 18πk.

Explanation of Solution

Write the expression for the energy stored in a magnetic field.

    U=cB2km        (4)

Here, c is the constant.

Write the expression for magnetic field inside the solenoid.

    B=4πkmkNIl

Substitute (4πkmkNIl) for B in equation (4).

    U=c(4πkmkNIl)2km        (5)

Write the expression of the energy stored in a solenoid.

    U=2πN2kmkI2l2        (6)

Conclusion:

Compare equation (5) and (6).

    c(4πkmkNIl)2km=2πN2kmkI2l2

Solve the above equation.

    c(4πkmkNI)2l2km=2πN2kmkI2l2c=18πk

Thus, the value of the constant is 18πk.

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Chapter 20 Solutions

General Physics, 2nd Edition

Ch. 20 - Prob. 11RQCh. 20 - Prob. 12RQCh. 20 - Prob. 13RQCh. 20 - Prob. 1ECh. 20 - Prob. 2ECh. 20 - Prob. 3ECh. 20 - Prob. 4ECh. 20 - Prob. 5ECh. 20 - Prob. 6ECh. 20 - Prob. 7ECh. 20 - Prob. 8ECh. 20 - Prob. 9ECh. 20 - Prob. 10ECh. 20 - Prob. 11ECh. 20 - Prob. 12ECh. 20 - Prob. 13ECh. 20 - Prob. 14ECh. 20 - Prob. 15ECh. 20 - Prob. 16ECh. 20 - Prob. 17ECh. 20 - Prob. 18ECh. 20 - Prob. 19ECh. 20 - Prob. 20ECh. 20 - Prob. 21ECh. 20 - Prob. 22ECh. 20 - Prob. 23ECh. 20 - Prob. 24ECh. 20 - Prob. 25ECh. 20 - Prob. 26ECh. 20 - Prob. 27ECh. 20 - Prob. 28ECh. 20 - Prob. 29ECh. 20 - Prob. 30ECh. 20 - Prob. 31ECh. 20 - Prob. 32ECh. 20 - Prob. 33ECh. 20 - Prob. 34ECh. 20 - Prob. 35ECh. 20 - Prob. 36ECh. 20 - Prob. 37ECh. 20 - Prob. 38ECh. 20 - Prob. 39ECh. 20 - Prob. 40ECh. 20 - Prob. 41ECh. 20 - Prob. 42ECh. 20 - Prob. 43ECh. 20 - Prob. 44ECh. 20 - Prob. 45ECh. 20 - Prob. 46ECh. 20 - Prob. 47ECh. 20 - Prob. 48ECh. 20 - Prob. 49ECh. 20 - Prob. 50ECh. 20 - Prob. 51ECh. 20 - Prob. 52ECh. 20 - Prob. 53ECh. 20 - Prob. 54ECh. 20 - Prob. 55ECh. 20 - Prob. 56ECh. 20 - Prob. 57ECh. 20 - Prob. 58ECh. 20 - Prob. 59ECh. 20 - Prob. 60ECh. 20 - Prob. 61ECh. 20 - Prob. 62ECh. 20 - Prob. 63ECh. 20 - Prob. 64ECh. 20 - Prob. 65ECh. 20 - Prob. 66ECh. 20 - Prob. 67ECh. 20 - Prob. 68ECh. 20 - Prob. 69ECh. 20 - Prob. 70ECh. 20 - Prob. 71ECh. 20 - Prob. 72ECh. 20 - Prob. 73ECh. 20 - Prob. 74ECh. 20 - Prob. 75ECh. 20 - Prob. 76ECh. 20 - Prob. 77ECh. 20 - Prob. 78ECh. 20 - Prob. 79ECh. 20 - Prob. 80ECh. 20 - Prob. 81ECh. 20 - Prob. 82ECh. 20 - Prob. 83ECh. 20 - Prob. 84ECh. 20 - Prob. 85ECh. 20 - Prob. 86ECh. 20 - Prob. 87ECh. 20 - Prob. 88ECh. 20 - Prob. 89ECh. 20 - Prob. 90ECh. 20 - Prob. 91ECh. 20 - Prob. 92ECh. 20 - Prob. 93ECh. 20 - Prob. 94ECh. 20 - Prob. 95E
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