Question

A block in the shape of a rectangular solid has a cross-sectional area of $3.50c{m}^2$ across its width, a front-to-rear length of $15.8$ cm, and a resistance of $935\Omega$. The block’s material contains $5.33\times {10}^{22}$ conduction electrons/$m^3$ . A potential difference of $35.8$ V is maintained between its front and rear faces. (a) What is the current in the block? (b) If the current density is uniform, what is its magnitude? What are (c) the drift velocity of the conduction electrons and (d) the magnitude of the electric field in the block?

Answer 1

(a) The current in the block is $i=V/R=35.8V/935\Omega =3.83\times {10}^{–2}A$.

(b) The magnitude of current density is $J=i/A=(3.83\times {10}^{–2}A)/(3.50\times {10}^{–4}{m}^2)=109A/m^2$ .

(c) $v_d=J/ne=\left({10}^{9}A/m^2\right)/\left[\right(5.33\times {10}^{22}/m^3\left)\right(1.60\times {10}^{–19}C\left)\right]=1.28\times {10}^{–2}m/s$.

(d) $E=V/L=35.8V/0.158m=227V/m$.