Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN: 9781133104261
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 20, Problem 7P

(a) Find the potential at a distance of 1.00 cm from a proton. (b) What is the potential difference between two points that are 1.00 cm and 2.00 cm from a proton? (c) Repeat parts (a) and (b) for an electron.

(a)

Expert Solution
Check Mark
To determine

The potential difference at a distance from proton.

Answer to Problem 7P

The potential difference at a distance from proton is 1.44×107V_.

Explanation of Solution

Write the equation for the potential difference.

  V1=kqr1        (I)

Here, V1 is the potential difference for first distance, k is Coulomb’s constant, q is charge and r1 is distance.

Conclusion:

Substitute 8.99×109N-m2/C2 for k, 1.6×1019C for q, 1.00cm for r1 in Equation (I) to find V1.

  V1=(8.99×109N-m2/C2)(1.6×1019C)[(1.00cm)(1×102m1cm)]=1.44×107V

Thus, the potential difference at a distance from proton is 1.44×107V_.

(b)

Expert Solution
Check Mark
To determine

The potential difference between the points from proton.

Answer to Problem 7P

The potential difference between the points from proton is 7.19×108V_.

Explanation of Solution

Write the expression for the potential difference between the points from proton.

(ΔV)=V2V1        (II)

Write the equation for the potential difference at a distance 1.00cm.

  V1=kqr1        (III)

Here, V1 is the potential difference for first distance, k is Coulomb’s constant, q is charge and r1 is distance.

Write the equation for the potential difference at a distance 2.00cm.

  V2=kqr2        (IV)

Here, V2 is the potential difference for second distance, k is Coulomb’s constant, q is charge and r2 is distance.

Rewrite the expression (II) by using (III) and (IV).

(ΔV)=(kqr2)(kqr1)        (V)

Conclusion:

Substitute 8.99×109N-m2/C2 for k, 1.6×1019C for q, 1.00cm for r1, 2.00cm for r2 in Equation (V) to find (ΔV).

(ΔV)=[(8.99×109N-m2/C2)(1.6×1019C)[(2.00cm)(1×102m1cm)]][(8.99×109N-m2/C2)(1.6×1019C)[(1.00cm)(1×102m1cm)]]=7.19×108V

Thus, the potential difference between the points from proton is 7.19×108V_.

(c)

Expert Solution
Check Mark
To determine

The potential difference at a distance from electron.

Answer to Problem 7P

The potential difference at a distance from electron is 1.44×107V_.

Explanation of Solution

Write the equation for the potential difference.

  V1=kqr1        (I)

Here, V1 is the potential difference for first distance, k is Coulomb’s constant, q is charge and r1 is distance.

Conclusion:

Substitute 8.99×109N-m2/C2 for k, 1.6×1019C for q, 1.00cm for r1 in Equation (I) to find V1.

  V1=(8.99×109N-m2/C2)(1.6×1019C)[(1.00cm)(1×102m1cm)]=1.44×107V

Thus, the potential difference at a distance from electron is 1.44×107V_.

(d)

Expert Solution
Check Mark
To determine

The potential difference between the points from electron.

Answer to Problem 7P

The potential difference between the points from electron is 7.19×108V_.

Explanation of Solution

Write the expression for the potential difference between the points from electron.

(ΔV)=V2V1        (II)

Write the equation for the potential difference at a distance 1.00cm.

  V1=kqr1        (III)

Here, V1 is the potential difference for first distance, k is Coulomb’s constant, q is charge and r1 is distance.

Write the equation for the potential difference at a distance 2.00cm.

  V2=kqr2        (IV)

Here, V2 is the potential difference for second distance, k is Coulomb’s constant, q is charge and r2 is distance.

Rewrite the expression (II) by using (III) and (IV).

(ΔV)=(kqr2)(kqr1)        (V)

Conclusion:

Substitute 8.99×109N-m2/C2 for k, 1.6×1019C for q, 1.00cm for r1, 2.00cm for r2 in Equation (V) to find (ΔV).

(ΔV)=[(8.99×109N-m2/C2)(1.6×1019C)[(2.00cm)(1×102m1cm)]][(8.99×109N-m2/C2)(1.6×1019C)[(1.00cm)(1×102m1cm)]]=7.19×108V

Thus, the potential difference between the points from electron is 7.19×108V_.

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Chapter 20 Solutions

Principles of Physics: A Calculus-Based Text

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