Question:

Current is flowing with a current density j=480Acm2j = 480 Acm ^{-2} in a copper wire. Assuming that each copper atom contributes one free electron and given that Avogadro number =6.0×1023atommol1= 6.0 \times 10^{23} \, atom \, mol^{-1} Density of copper =9.0gcm2 = 9.0 \, g \, cm^{-2} \, Electronic charge =1.6×1019C = 1.6 \times 10^{-19} C Atomic weight of copper =64gmol1= 64 \, g \, mol^{-1} The drift velocity of electrons is

Updated On: Jun 8, 2024
  • 1mms11 mm \, s^{-1}
  • 2mms12 mm \, s^{-1}
  • 0.5mms10.5 mm \, s^{-1}
  • 0.36mms10.36 mm \, s^{-1}
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The Correct Option is D

Solution and Explanation

Drift velocity is given by
        vd=InqA \, \, \, \, \, \, \, \, v_d = \frac {I}{nqA}
where I is current, n the number of electrons, A the area, q the charge.
Given IA=480Acm2andq=1.6×1019C \frac {I}{A} = \frac {480A}{cm^2} \, and \, q = 1.6 \times 10^{-19}C
     n=6×1023×964 \, \, \, \, \, n = \frac {6 \times 10^{23}\times 9} {64}
     vd=480×646×1023×9×1.6×1019\therefore \, \, \, \, \, v_d = 480 \times \frac {64}{6 \times 10^{23}\times 9 \times 1.6 \times 10^{-19}}
    vd=480×646×9×1.6×10000cms19\Rightarrow \, \, \, \, v_d = \frac {480 \times 64}{6 \times 9 \times 1.6 \times 10000}cms^{-19}
    vd=32900cms1\Rightarrow \, \, \, \, v_d = \frac {32}{900}cms^{-1}
     =32×10900cms1\, \, \, \, \, = \frac {32 \times 10}{900}cms^{-1}
        =0.36mms1 \, \, \, \, \, \, \, \, = 0.36 mms^-1
        vd=0.36mms1\Rightarrow \, \, \, \, \, \, \, \, v_d = 0.36 \, mms^-1
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Concepts Used:

Electromagnetic Induction

Electromagnetic Induction is a current produced by the voltage production due to a changing magnetic field. This happens in one of the two conditions:-

  1. When we place the conductor in a changing magnetic field.
  2. When the conductor constantly moves in a stationary field.

Formula:

The electromagnetic induction is mathematically represented as:-

e=N × d∅.dt

Where

  • e = induced voltage
  • N = number of turns in the coil
  • Φ = Magnetic flux (This is the amount of magnetic field present on the surface)
  • t = time

Applications of Electromagnetic Induction

  1. Electromagnetic induction in AC generator
  2. Electrical Transformers
  3. Magnetic Flow Meter