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 36P
To determine

The speed of the proton.

Expert Solution & Answer
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Answer to Problem 36P

The speed of the proton is 5.94×105m/s.

Explanation of Solution

Write the expression for the total enclosed charge.

    Qenc=(ρ43π(r13r23))+q                                                                                       (I)

Here, Qenc is the total enclosed charge, ρ is the volume charge density, r1 and r2 is the outer and inner radius respectively and q is charge of the particle.

Write the expression for electric field force on the proton.

    F=eE                                                                                                                     (II)

Here, F is the electric field force on the proton, e is the charge of the proton and E is the electric field.

Substitute Qenc4πε0r12 for E in equation (II) to calculate F.

    F=e(Qenc4πε0r12)                                                                                                      (III)

Write the expression for centripetal force acting on the proton.

    F=mp×v2r1                                                                                                             (IV)

Here, mp is the mass of the proton, v is the velocity of the proton, r1 is the orbit radius, F is the centripetal force acting on the proton.

From Equation (III) and Equation (IV),

    e(Qenc4πε0r12)=mpv2r1

Rewrite the above equation for v.

    e(Qenc4πε0r12)=mpv2r1v2=e(r1mp)(Qenc4πε0r12)v=e(r1mp)(kQencr12)                                                                                (V)

Conclusion:

Substitute 1.33μC/m3 for ρ, 20.0cm for r2, 25.0cm for r1 and 60.0nC for q in equation (I) to calculate Qenc.

    Qenc=(1.33μC/m3)(43)π[(25.0cm)3(20.0cm)3]+(60.0nC)=[((1.33μC/m3)(1C106μC)×(43)π×(15625cm38000cm3)(1×102m1cm)3)+(60nC)(1×109C1nC)]=((1.33×106C/m3)(43)π(7.625×103m3))+(60×109C)=(0.0425×106C)+(60×109C)

Further solve the above equation.

    Qenc=1.025×107C

Substitute 1.6×1019C for e, 1.025×107C for Qenc, 9×109Nm2/C2 for k, 1.67×1027Kg for mp, 0.25m for r1 in equation (V) to calculate v.

    v=(1.6×1019C)(1.025×107C)(0.25m)(9×109Nm2/C2)(1.67×1027kg)(0.25m)2=(1.6×1019C)230.625Nm3/C1.044×1028kgm2=35.35×1010m2/s2=5.94×105m/s

Therefore, the velocity of the proton is 5.94×105m/s.

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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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