A current of 5 A is passing through a non-linear magnesium wire of cross-section 0.04 m². At every point the direction of current density is at an angle of 60$^\circ$ with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is :

(Resistivity of magnesium $\rho$ = 44 $\times$ 10^$-$8 $\Omega$m)

Given, current, I = 5A<br/><br/>Area of cross-section of wire, A = 0.04 m²<br/><br/>We know that, $J = {I \over A}$<br/><br/>$\Rightarrow I = JA$<br/><br/>or $I = J\,.\,A$ or $I = JA\cos \theta$<br/><br/>where, J = current density.<br/><br/>$\Rightarrow 5 = J\left( {{4 \over {100}}} \right) \times \cos (60^\circ )$ [$\because$ Given, $\theta$ = 60$^\circ$]<br/><br/>$J = 500 \times {1 \over 2}$ [$\because$ cos60$^\circ$ = ${1 \over 2}$]<br/><br/>$\Rightarrow$ J = 250 Am^$-$2<br/><br/>The relation between electric field, current density and resistivity can be given as,<br/><br/>E = $\rho$ . J<br/><br/>= 44 $\times$ 10^$-$8 $\times$ 250 [$\because$ Resistivity, $\rho$ = 44 $\times$ 10^$-$8 $\Omega$-m]<br/><br/>= 11 $\times$ 10^$-$5 V/m