A current of 5 A passes through a copper conductor (resistivity $=1.7 \times 10^{-8} \Omega \mathrm{~m}$) of radius of cross-section 5 mm. Find the mobility of the charges if their drift velocity is 1.1 $\times 10^{-3} \mathrm{~m} / \mathrm{s}$.

(B) $1.0 \mathrm{~m}^{2} / \mathrm{Vs}$

(A) $1.8 \mathrm{~m}^{2} / \mathrm{Vs}$

(C) $1.3 \mathrm{~m}^{2} / \mathrm{Vs}$

(D) $1.5 \mathrm{~m}^{2} / \mathrm{Vs}$

JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Current Electricity

A current of 5 A passes through a copper conductor (resistivity

= 1.7 \times 1 0^{- 8} Ω m

) of radius of cross-section 5 mm. Find the mobility of the charges if their drift velocity is 1.1

\times 1 0^{- 3} m / s

Answer: (B)

Mobility is

μ = \frac{v _{d}}{E}

, and the field follows from

E = ρ J

with current density

J = \frac{I}{A}

. The wire's cross-section is

A = π r^{2} = π (5 \times 1 0^{- 3})^{2} = 25 π \times 1 0^{- 6}

^{2}

, so

J = \frac{5}{25 π \times 1 0 ^{- 6}}

A/m

^{2}

and

E = 1.7 \times 1 0^{- 8} J

. Putting the pieces together,

μ = \frac{1.1 \times 1 0 ^{- 3} \times 25 π \times 1 0 ^{- 6}}{1.7 \times 1 0 ^{- 8} \times 5} \approx 1.0

^{2}

\cdot

JEE Main · 2019 · 10 Apr 2019 · Shift 1 · Single correct option