A wire has a current density of 17.0 A/mm 2 . If Thedrift velocity is 4.0 x 10 -

Question

A wire has a current density of 17.0 A/mm2. If Thedrift velocity is 4.0 x 10-8 m/s, how manyfree electrons does the wire have in a 1.0 m length? Theradius of the wire is 1.0 mm.
A) 5.2 x 1046 B) 1.7 x 1052 C) 8.3 x 1027 D) 2.7 x 1033 A wire has a current density of 17.0 A/mm2. If Thedrift velocity is 4.0 x 10-8 m/s, how manyfree electrons does the wire have in a 1.0 m length? Theradius of the wire is 1.0 mm.
A) 5.2 x 1046 B) 1.7 x 1052 C) 8.3 x 1027 D) 2.7 x 1033 B) 1.7 x 1052 C) 8.3 x 1027 D) 2.7 x 1033

Explanation / Answer

current density J = 17.0 A/mm2                          = 17 * 10 ^ 6 A / m ^ 2 drift velocity v = 4.0 x 10-8 m/s Length L = 1.0 m The radius of the wire r = 1.0 mm.                                     = 10 ^ -3 m Volume V = r ^ 2 L                 = 3.14 * 10^-6 m ^ 3 we know J = nq v where q = charge of electron = 1.6 * 10 ^ -19 C from this density( No.of electrons per unit volume) n =J / vq                                                                                = 2.656 * 10 ^ 33 / m ^ 3 So, No.of electrons in the volume V is = n V                                                           = 8.344* 10 ^ 27                          = 17 * 10 ^ 6 A / m ^ 2 drift velocity v = 4.0 x 10-8 m/s Length L = 1.0 m The radius of the wire r = 1.0 mm.                                     = 10 ^ -3 m Volume V = r ^ 2 L                 = 3.14 * 10^-6 m ^ 3 we know J = nq v where q = charge of electron = 1.6 * 10 ^ -19 C from this density( No.of electrons per unit volume) n =J / vq                                                                                = 2.656 * 10 ^ 33 / m ^ 3 So, No.of electrons in the volume V is = n V                                                           = 8.344* 10 ^ 27

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