Question

An infinite line charge of uniform linear charge de sity λ--2.3 μC/m lies parallel to the y axis at x--2 m. A pont charge of 3.6 μC is located at x = 2.5 m, y = 3.5 m. Find the x component of the electric field at x 3.5 m,y-3.0 m. kN/C Enter Help

Answer 1

Electric field due to infinite line charge is given by

$E=\frac{2k\lambda }{r}$

$\overrightarrow{E_{1}}=\frac{2\times (9\times 10^{9})(2.3\times 10^{-6})}{3.5}\left ( -\widehat{i} \right )=-11828.57 \widehat{i}N/C$

Electric field due to point charge

$\overrightarrow{E}=\frac{KQ}{|r|^{2}}\widehat{r}$

r=(3.5-2.5)i + (3-3.5)j =i-0.5j

$\left | \overrightarrow{r} \right |=\sqrt{1^{2}+(-0.5)^{2}}=1.118 m$

$\widehat{r}=\frac{\widehat{i}-0.5\widehat{j}}{1.118}=0.8944\widehat{i}-0.4472\widehat{j}$

$\overrightarrow{E_{2}}=\left ( \frac{(9\times 10^{9})(3.6\times 10^{-6})}{1.25} \right )\times (0.8944\widehat{i}-0.4472\widehat{j})=(23183.55\widehat{i}+11591.78\widehat{j})N/C$

The X-component of electric field

E_x=-11828.57+23183.55=11355 N/C

E_x=11.355 KN/C