Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Textbook Question
Chapter 10, Problem 1P

a. Find the electric field strength at a point 1 m from a charge of 4 μC .

b. Find the electric field strength at a point 1 mm [1/1000 the distance of part (a)] from the same charge as part (a) and compare results.

Expert Solution
Check Mark
To determine

(a)

The electric field strength at a point 1 m from a charge of 4 μC.

Answer to Problem 1P

The electric field strength at a point 1 m from a charge of 4 μC is 35.97×103 N/C.

Explanation of Solution

Given:

The distance is 1 m.

The charge is 4 μC.

Concept used:

Expression for the electric filed due to a point charge.

E=Q4πε0r2 ..... (1)

Here, E is electric field, Q is the charge and ε0 is the permittivity of free space.

Calculation:

Substitute 4 μC for Q, 8.85×1012 C2/Nm2 for ε0 and 1 m for r in equation (1).

  E=4 μC4π( 8.85× 10 12  C 2 /Nm 2 ) ( 1 m )2=4 μC( 1 C 10 6  μC )4π( 8.85× 10 12  C 2 /Nm 2 ) ( 1 m )2=4× 10 6 C4π( 8.85× 10 12  C 2 /Nm 2 ) ( 1 m )2=3.59×104 N/C

Conclusion:

Thus, the electric field strength at a point 1 m from a charge of 4 μC is 35.97×103 N/C.

Expert Solution
Check Mark
To determine

(b)

The electric field strength at a point 1 mm from a charge of 4 μC. Also, compare the results with the answer obtained in part (a).

Answer to Problem 1P

The electric field strength at point 1 mm is 3.59×1010 N/C and the electric field strength at point 1 mm is 106 times greater than the electric field strength at a point 1 m from a charge of 4 μC.

Explanation of Solution

Given:

The distance is 1 mm.

The charge is 4 μC.

Calculation:

Substitute 4 μC for Q, 8.85×1012 C2/Nm2 for ε0 and 1 mm for r in equation (1).

  E=4 μC4π( 8.85× 10 12  C 2 /Nm 2 ) ( 1 mm )2=4 μC( 1 C 10 6  μC )4π( 8.85× 10 12  C 2 /Nm 2 ) ( 1 mm( 1 m 1000 mm ) )2=4× 10 6 C4π( 8.85× 10 12  C 2 /Nm 2 ) ( 10 3  m )2=3.59×1010 N/C

Therefore, the electric field strength at a point 1 mm is 106 times greater than the electric field strength at a point 1 m from a charge of 4 μC

Conclusion:

Thus, the electric field strength at point 1 mm is 3.59×1010 N/C and the electric field strength at point 1 mm is 106 times greater than the electric field strength at point 1 m from a charge of 4 μC.

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Chapter 10 Solutions

Introductory Circuit Analysis (13th Edition)

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