Question

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Answer 1

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A block in the shape of a rectangular solid has a cross-sectionalarea of 3.00 cm² across itswidth, a front-to-rear length of 15.5 cm,and a resistance of 925 . Thematerial of which the block is made has 5.33 10²² conductionelectrons/m³. A potential difference of 35.7 V is maintained between its front and rearfaces.

(a) What is the current in the block?
1 A

(b) If the current density is uniform, what is its magnitude?
2 A/m²

(c) What is the drift velocity of the conduction electrons?
3 m/s

(d) What is the magnitude of the electric field in the block?
4 V/m

a.   Current   I   =   V/ R

                              =   35.7/ 925

                              =   0.0386   A

   b.   Currentdensity   J   =   I/ A

                                       =   0.0386/ 3.0 cm²

                                       =   0.0386/ 3.0 * 10^-4

                                       =   1.287* 10²   A/m²

   c.   J   =   n* e * v_d

         driftvelocity   v_d   =   J/ n * e

   n   =   electronconcentration   =   5.33 *10²²   /m³

   e   =   chargeon one electron   =   1.6 *10^-19   C

         =>   v_d   =   1.287* 10² / 5.33 * 10²² * 1.6 * 10^-19

                     =   1.509* 10^-2   m/s

   c.   Electricfield   E   =   V /l

      l   =   length

      E   =   35.7/ 15.5 cm

            =   35.7/ 0.155

            =   2.303* 10²   V/m