At a distance of 3.5 cm from the center of a very long uniformly charged wire, the electric field has magnitude 2000 N/C and is directed toward the wire. What is the charge on a 1.0 cm length of wire near the center?

The electric field strength from a very long (essentially infinitely long) uniformly charged wire is given by:

E = λ / (2πrε₀)

E = electric field strength, λ = linear charge density, r = distance from wire

Given values:

E = 2000N/C, r = 3.5*10⁻²m

Plug in and solve for λ:

2000 = λ / (2π (3.5*10⁻²) (8.85*10⁻¹²))

λ = 3.9*10⁻⁹C/m

The amount of charge on a certain length of this wire is given by:

Q = λL

Q = charge, λ = charge density, L = length

Given values:

λ = 3.9*10⁻⁹C/m, L = 1.0*10⁻²m

Plug in and solve for Q:

Q = 3.9*10⁻⁹ (1.0*10⁻²)

Q = 3.9*10⁻¹¹C