First slide

Finding field strength using Gauss's Law

Question

An infinitely long wire is kept along z-axis from $z = - \infty$ to $z = + \infty$ having uniform near charge density $\frac{10}{9} nC / m$ . The electric field at point (6 cm, 8 cm, 10 cm) will be

Difficult

A

$(120 \hat{i} + 160 \hat{j} + 200 \hat{k}) V / m$
B

$200 \hat{k} V / m$
C

$(160 \hat{i} + 120 \hat{j}) V / m$
D

$(120 \hat{i} + 160 \hat{j}) V / m$

Solution

$\begin{matrix} E = \frac{λ}{2 {πε}_{0} d} = \frac{2 Kλ}{d} \\ = \frac{2 \times 9 \times 10^{9} \times (10 / 9) \times 10^{- 9}}{10 \times 10^{- 2}} = 200 V / m \end{matrix}$
As field is radially out, there is no component of it in z direction.
$\begin{matrix} \vec{E} = (200 \cos 53^{\circ} \hat{i} + 200 \sin 53^{\circ} \hat{j}) V / m \\ = (200 \times \frac{3}{5} \hat{i} + 200 \times \frac{4}{5} \hat{j}) = (120 \hat{i} + 160 \hat{j}) V / m \end{matrix}$

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