Question

This question checks that you can use the formula of the electric field due to a long, thin wire with charge on it. The field due to an infinitely long, thin wire with linear charge density LaTeX: \lambda λ is LaTeX: \vec{E} = \frac{1}{4\pi\epsilon_0}\frac{2\lambda}{r}\hat{r}E → = 1 4 π ϵ 0 2 λ r r ^. Imagine a long, thin wire with a constant charge per unit length of -6.6LaTeX: \times10^{-7}× 10 − 7 C/m. What is the magnitude of the electric field at a point 10 cm from the wire (assuming that the point is much closer to the wire's nearest point than to either of its ends)? Give your answer in units of kN/C.

Answer 1

E = -118 KN / C

Step-by-step explanation:

In this exercise we are given the expression of the electric field for a wire

E = 1 /4πε₀ 2λ / r

they also indicate the linear density of charge

λ = 6,6 10⁻⁷ C / m

ask to calculate the electric field at a position at r = 10 cm from the wire

k = 1 /4πε₀ = 8,988 10⁹ N m² / C²

E = 8,988 10⁹ 2 (-6.6 10⁻⁷ / 0.10)

E = -1.18 105 N / C

we reduce to KN / C

1 KN / C = 10³ N / C

E = -1.18 10² KN / C

E = -118 KN / C

the negative sign indicates that the field is directed to the charged