At a distance of 4.3 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? (ε0 = 8.85 × 10^-12 C²/N ∙ m²)

Question

Quizplus · Accepted Answer

The magnitude of electric field due to a uniformly charged long wire, at a distance r from the center of the wire is given by:

E = λ/(2πε0r)

where λ is the linear charge density of the wire.

Rearranging the equation, we get:

λ = 2πε0rE

Substituting the given values, we get:

λ = 2π(8.85×10^⁻12 N∙m²/C²)(0.043m)(2000 N/C)

λ = -0.019 C/m

The charge on a 1.0 cm length of wire is given by:

q = λL

where L is the length of wire.

Substituting the values, we get:

q = (-0.019 C/m)(0.01 m)

q = -0.00019 C

Thus, the answer is -0.048 nC (since 1 nC = 10^-9 C).

At a Distance of 4