# A -12 nC charrge is located at the origin. a) What

A -12 nC charrge is located at the origin.
a) What is the strength of the electric field at the position $$\displaystyle{\left({x},{y}\right)}={\left({0}{c}{m},{5.0}{c}{m}\right)}?$$
b)What is the strength of the electric field at the position $$\displaystyle{\left({x},{y}\right)}={\left(-{5.0}{c}{m},-{5.0}{c}{m}\right)}?$$
c)What is the strength of the electric field at the position $$\displaystyle{\left({x},{y}\right)}={\left(-{5.0}{c}{m},{5.0}{c}{m}\right)}?$$

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kaluitagf

Step 1
The charge located at the origin is given as,
$$\displaystyle{q}=-{12}{n}{C}$$
$$\displaystyle=-{12}{n}{C}\times{\frac{{{10}^{{-{9}}}{C}}}{{{1}{n}{C}}}}$$
$$\displaystyle=-{12}\times{10}^{{-{9}}}{C}$$
Step 2
(a)
The position at which electric field required is given as,
$$\displaystyle{\left({x},{y}\right)}={\left({0}{c}{m},{5}{c}{m}\right)}$$
The distance of the required position from the origin can be determined as,
$$\displaystyle{r}=\sqrt{{{x}^{{{2}}}+{y}^{{{2}}}}}$$
$$\displaystyle=\sqrt{{{\left({0}{c}{m}\right)}^{{{2}}}+{\left({5}{c}{m}\right)}^{{{2}}}}}$$
$$\displaystyle={5}{c}{m}\times{\frac{{{10}^{{-{2}}}{m}}}{{{1}{c}{m}}}}$$
$$\displaystyle={0.05}{c}{m}$$
The electric field strength at the required location can be determined as,
$$E=\frac{k\mid q\mid}{r^{2}}$$
$$=\frac{(9\times10^{9}N.m^{2}/C^{2})\mid-12\times10^{-9}C\mid}{(0.05m)^{2}}$$
$$\displaystyle={43200}\frac{{N}}{{C}}$$

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Step 3
(b)
The position at which electric field required is given as,
$$\displaystyle{\left({x},{y}\right)}={\left(-{5}{c}{m},-{5}{c}{m}\right)}$$
The distance of the required position from the origin cam be determined as,
$$\displaystyle{r}=\sqrt{{{x}^{{{2}}}+{y}^{{{2}}}}}$$
$$\displaystyle=\sqrt{{{\left(-{5}{c}{m}\right)}^{{{2}}}+{\left(-{5}{c}{m}\right)}^{{{2}}}}}$$
$$\displaystyle={7.1}{c}{m}\times{\frac{{{10}^{{-{2}}}{m}}}{{{1}{c}{m}}}}$$
$$\displaystyle={0.071}{c}{m}$$
The electric field strength at the required location can be determined as,
$$E=\frac{k\mid q\mid}{r^{2}}$$
$$=\frac{(9\times10^{9}N.m^{2}/C^{2})\mid-12\times10^{-9}C\mid}{(0.071m)^{2}}$$
$$\displaystyle={21424.3}\frac{{N}}{{C}}$$

star233

Step 4
(b)
The position at which electric field required is given as,
$$(x,y)=(-5cm,5cm)$$
The distance of the required position from the origin cam be determined as,
$$r=\sqrt{x^{2}+y^{2}} \\=\sqrt{(-5cm)^{2}+(5cm)^{2}} \\=7.1cm\times\frac{10^{-2}m}{1cm} \\=0.071cm$$
The electric field strength at the required location can be determined as,
$$E=\frac{k\mid q\mid}{r^{2}} \\=\frac{(9\times10^{9}N.m^{2}/C^{2})\mid-12\times10^{-9}C\mid}{(0.071m)^{2}} \\=21424.3N/C$$