Question

| 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?

Answer 1

Answer:

The charge is 0.056 nC.

Explanation:

Given that,

Electric field = 2000 N/C

Distance = 5.0 cm

We need to calculate the charge density

Using formula of charge density

$E=\dfrac{\lambda}{2\pi\times\epsilon_{0}r}$

$\lambda=2\pi\times\epsilon_{0}\times r\times E$

Put the value into the formula

$\lambda=2\pi\times8.85\times10^{-12}\times5.0\times10^{-2}\times2000$

$\lambda=5.56\times10^{-9}\ C/m$

We need to calculate the charge in 1.0 cm

Using formula of charge

$Charge = \lambda\times\text{length of segment}$

$Charge =5.56\times10^{-9}\times1.0\times10^{-2}$

$Charge=0.056\times10^{-9}\ C$

$Charge=0.056\ nC$

Hence, The charge is 0.056 nC.