Chapter 23: Q. 12 (page 653)

The electric field $5.0 cm$ from a very long charged wire is ( $2000 N / C$ , toward the wire). What is the charge (in $nC$ ) on a $1.0$ -cm-long segment of the wire $?$

Short Answer

Expert verified

The charge on a segment of the wire is $- 0.0556 nC$ .

Step by step solution

Formula for linear charge density

Electric field,

$E = \frac{λ}{2 {πε}_{0} r}$

Linear charge density,

$λ = \frac{q}{l}$

Given segment $∆ l$ , the linear charge density will be:

$λ = \frac{q}{Δl}$

Derivation for charge

Electric field,

$E = \frac{(\frac{q}{Δl})}{2 {πε}_{0} r}$

$E = \frac{q}{(Δl) 2 {πε}_{0} r}$

Rearrange the value,

$q = (Δl) 2 {πε}_{0} r \cdot E$

Calculation of of the wire

Charge is,

$q = (0.01 m) 2 π (8.85 \times 10^{- 12} \frac{C^{2}}{N \cdot m^{2}}) (0.05 m) (2000 \frac{N}{C})$

$= 5.56 \times 10^{- 11} C$

$q = (5.56 \times 10^{- 11} C) \cdot (\frac{1.0 \times 10^{9} nC}{1 C}) = 0.0556 nC$

Because the electric field is oriented toward the wire, the charge on the wire will have a negative charge.

$q = - 0.0556 nC$

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The electric field $5.0 cm$ from a very long charged wire is ( $2000 N / C$ , toward the wire). What is the charge (in $nC$ ) on a $1.0$ -cm-long segment of the wire $?$

Short Answer

Step by step solution

Formula for linear charge density

Derivation for charge

Calculation of of the wire

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The electric field 5.0cmfrom a very long charged wire is ( 2000N/C, toward the wire). What is the charge (in nC) on a 1.0-cm-long segment of the wire?

Short Answer

Step by step solution

Formula for linear charge density

Derivation for charge

Calculation of of the wire

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Thermodynamics

Astrophysics

Kinematics Physics

Work Energy and Power

Electrostatics

Measurements

Study anywhere. Anytime. Across all devices.

The electric field $5.0 cm$ from a very long charged wire is ( $2000 N / C$ , toward the wire). What is the charge (in $nC$ ) on a $1.0$ -cm-long segment of the wire $?$