Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
9th Edition
ISBN: 9781305372337
Author: Raymond A. Serway | John W. Jewett
Publisher: Cengage Learning
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Chapter 24, Problem 55AP
To determine

The graph of the magnitude of electric field due to the given configuration versus r for 0<r<25.0cm.

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Answer to Problem 55AP

The graph of the magnitude of electric field due to the given configuration versus r for 0<r<25.0cm is shown in figure below.

Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University, Chapter 24, Problem 55AP , additional homework tip  1

Explanation of Solution

Write the expression to calculate the electric field on uniformly charged sphere for r<R.

    E=kerQR3                       (I)

Here, E is the electric field, Q is the charge, ke is the Coulomb’s constant R is the radius of insulating sphere and r is the distance between the point.

Write the expression to calculate the electric field on uniformly charged sphere for rR.

    E=keQr2                       (II)

The electric field inside a conductor is 0.

So, for the region 10.00cm<r<15.00cm.

    E=0.

Write the expression to calculate the net charge outside the sphere.

    Qnet=QoutQ                     (III)

Here, Qnet is the net charge, Q is the charge inside the sphere, Qout is the charge outside the sphere.

 Write the expression to calculate the electric field outside the uniformly charged sphere.

    E=keQoutr2                    (IV)

Conclusion:

For r5.00cm

Assume r=2.50cm.

Substitute 9×109N-m2/C2 for ke, 2.50cm for r, 3.00μC for Q and 5.00cm for R in equation (I) to solve for E.

    E=9×109N-m2/C2(2.50cm×102m1cm)(3.00μC×106C1μC)(5.00cm×102m1cm)3=5.4×106N/C×106MN1N=5.4MN/C

Calculate the electric field at r=5.00cm.

Substitute 9×109N-m2/C2 for ke, 5.00cm for r, 3.00μC for Q and 5.00cm for R in equation (II) to solve for E.

    E=9×109N-m2/C2(5.00cm×102m1cm)(3.00μC×106C1μC)(5.00cm×102m1cm)3=10.8×106N/C×106MN1N=10.8MN/C

For region 5.00cm<r<10.00cm.

At r=7.50cm

Substitute 9×109N-m2/C2 for ke, 7.50cm for r, 3.00μC for Q in equation (II) to solve for E.

    E=9×109N-m2/C2(3.00μC×106C1μC)(7.50cm×102m1cm)2=4.8×106N/C×106MN1N=4.8MN/C

At r=10.00cm,

Substitute 9×109N-m2/C2 for ke, 10.00cm for r, 3.00μC for Q in equation (II) to solve for E.

    E=9×109N-m2/C2(3.00μC×106C1μC)(10.00cm×102m1cm)2=2.7×106N/C×106MN1N=2.7MN/C

For region r>15.00cm,

Substitute 1.00μC for Qnet, 3.00μC for Q in equation (III) to solve for Qout.

    1.00μC=QoutQout=2.00μC

At r=25.00cm,

    E=9×109N-m2/C2(2.00μC×106C1μC)(25.00cm×102m1cm)2=0.288×106N/C×106MN1N=0.288MN/C

The graph of the magnitude of electric field due to the given configuration versus r for 0<r<25.0cm is shown in figure below.

Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University, Chapter 24, Problem 55AP , additional homework tip  2

Figure (1)

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Chapter 24 Solutions

Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University

Ch. 24 - Prob. 9OQCh. 24 - Prob. 10OQCh. 24 - Prob. 11OQCh. 24 - Prob. 1CQCh. 24 - Prob. 2CQCh. 24 - Prob. 3CQCh. 24 - Prob. 4CQCh. 24 - Prob. 5CQCh. 24 - Prob. 6CQCh. 24 - Prob. 7CQCh. 24 - Prob. 8CQCh. 24 - Prob. 9CQCh. 24 - Prob. 10CQCh. 24 - Prob. 11CQCh. 24 - A flat surface of area 3.20 m2 is rotated in a...Ch. 24 - A vertical electric field of magnitude 2.00 104...Ch. 24 - Prob. 3PCh. 24 - Prob. 4PCh. 24 - Prob. 5PCh. 24 - A nonuniform electric field is given by the...Ch. 24 - An uncharged, nonconducting, hollow sphere of...Ch. 24 - Prob. 8PCh. 24 - Prob. 9PCh. 24 - Prob. 10PCh. 24 - Prob. 11PCh. 24 - A charge of 170 C is at the center of a cube of...Ch. 24 - Prob. 13PCh. 24 - A particle with charge of 12.0 C is placed at the...Ch. 24 - Prob. 15PCh. 24 - Prob. 16PCh. 24 - Prob. 17PCh. 24 - Find the net electric flux through (a) the closed...Ch. 24 - Prob. 19PCh. 24 - Prob. 20PCh. 24 - Prob. 21PCh. 24 - Prob. 22PCh. 24 - Prob. 23PCh. 24 - Prob. 24PCh. 24 - Prob. 25PCh. 24 - Determine the magnitude of the electric field at...Ch. 24 - A large, flat, horizontal sheet of charge has a...Ch. 24 - Prob. 28PCh. 24 - Prob. 29PCh. 24 - A nonconducting wall carries charge with a uniform...Ch. 24 - A uniformly charged, straight filament 7.00 m in...Ch. 24 - Prob. 32PCh. 24 - Consider a long, cylindrical charge distribution...Ch. 24 - A cylindrical shell of radius 7.00 cm and length...Ch. 24 - A solid sphere of radius 40.0 cm has a total...Ch. 24 - Prob. 36PCh. 24 - Prob. 37PCh. 24 - Why is the following situation impossible? A solid...Ch. 24 - A solid metallic sphere of radius a carries total...Ch. 24 - Prob. 40PCh. 24 - A very large, thin, flat plate of aluminum of area...Ch. 24 - Prob. 42PCh. 24 - Prob. 43PCh. 24 - Prob. 44PCh. 24 - A long, straight wire is surrounded by a hollow...Ch. 24 - Prob. 46PCh. 24 - Prob. 47PCh. 24 - Prob. 48APCh. 24 - Prob. 49APCh. 24 - Prob. 50APCh. 24 - Prob. 51APCh. 24 - Prob. 52APCh. 24 - Prob. 53APCh. 24 - Prob. 54APCh. 24 - Prob. 55APCh. 24 - Prob. 56APCh. 24 - Prob. 57APCh. 24 - An insulating solid sphere of radius a has a...Ch. 24 - Prob. 59APCh. 24 - Prob. 60APCh. 24 - Prob. 61CPCh. 24 - Prob. 62CPCh. 24 - Prob. 63CPCh. 24 - Prob. 64CPCh. 24 - Prob. 65CPCh. 24 - A solid insulating sphere of radius R has a...Ch. 24 - Prob. 67CPCh. 24 - Prob. 68CPCh. 24 - Prob. 69CP
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