Question

A potential difference of 3.00 nV is set up across a 2.00 cm length of copper wire that has a radius of 2.00 mm. How much charge drifts through a cross section in 3.00 ms

Answer 1

The number of charge drifts are 3.35 X 10⁻⁷C

Explanation:

Given:

Potential difference, V = 3 nV = 3 X 10⁻⁹m

Length of wire, L = 2 cm = 0.02 m

Radius of the wire, r = 2 mm = 2 X 10⁻³m

Cross section, 3 ms

charge drifts, q = ?

We know,

the charge drifts through the copper wire is given by

q = iΔt

where Δt = 3 X 10⁻³s

and i = $\frac{V}{R}$

where R is the resistance

R = $\frac{pL}{r^{2} \pi }$

ρ is the resistivity of the copper wire = 1.69 X 10⁻⁸Ωm

So, i = $\frac{\pi(r)^{2}V }{pL}$

q = $\frac{\pi(r^{2} )Vt }{pL}$

Substituting the values,

q = 3.14 X (0.02)² X 3 X 10⁻⁹ X 3 X 10⁻³ / 1.69 X 10⁻⁸ X 0.02

q = 3.35 X 10⁻⁷C

Therefore, the number of charge drifts are 3.35 X 10⁻⁷C