A 1 m long copper wire carries a current of 1 A. If the cross section of the wire is $2.0 \mathrm{~mm}^{2}$ and the resistivity of copper is $1.7 \times 10^{-8} \Omega \mathrm{~m}$, the force experienced by moving electron in the wire is $\_\_\_\_$ $\times 10^{-23} \mathrm{~N}$. (charge on electron $=1.6 \times 10^{-19} \mathrm{C}$)

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Current Electricity

A 1 m long copper wire carries a current of 1 A. If the cross section of the wire is

2.0 mm^{2}

and the resistivity of copper is

1.7 \times 1 0^{- 8} Ω m

, the force experienced by moving electron in the wire is

____

\times 1 0^{- 23} N

. (charge on electron

= 1.6 \times 1 0^{- 19} C

)

Answer: 136

The force on an electron in the wire is

F = e E

, where

E

is the electric field. The electric field is related to the potential difference by

E = V / l

. Using Ohm's law,

V = I R

, where

R = ρl / A

.

Given:

l = 1

i = 1

A = 2 \times 1 0^{- 6}

m²,

ρ = 1.7 \times 1 0^{- 8} Ω

e = 1.6 \times 1 0^{- 19}

C.

Resistance:

R = \frac{ρl}{A} = \frac{1.7 \times 1 0 ^{- 8} \times 1}{2 \times 1 0 ^{- 6}} = 8.5 \times 1 0^{- 3} Ω

Voltage:

V = i R = 1 \times 8.5 \times 1 0^{- 3} = 8.5 \times 1 0^{- 3}

V

Electric field:

E = V / l = 8.5 \times 1 0^{- 3}

V/m

Force:

F = e E = 1.6 \times 1 0^{- 19} \times 8.5 \times 1 0^{- 3} = 1.36 \times 1 0^{- 21}

= 136 \times 1 0^{- 23}

N

Therefore, the answer is 136.

JEE Main · 2022 · 27 Jul 2022 · Shift 1 · Integer answer