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A +11 nC charge is located at the origin. Part A) What is the electric field at the position (x2,...

Question:

A +11 nC charge is located at the origin.

Part A) What is the electric field at the position {eq}(x_2, y_2) {/eq} = (-5.0 cm, 5.0 cm)? Write the electric field vector in component form.

Part B) What is the electric field at the position {eq}(x_3, y_3) {/eq} = (-5.0 cm, -5.0 cm)? Write the electric field vector in component form.

Part C) Draw a field diagram showing the electric field vectors at these points.

Electric Field:

An electric charge can exert electric fields of equal magnitude at different points on the plane. The difference that makes each electric field is the structure of its components, taking into account that the electric field is a vector quantity. In this way there can be 3 electric fields with different components but with equal magnitudes due to the same electric charge.

Answer and Explanation: 1

Data:

{eq}\textrm{Coulomb's Constant:}\:k=9\times 10^{9}\:\frac{Nm^2}{C^2} \\ \textrm{Charge:}\:Q=+11\:\eta C=+11\times 10^{-9}\:C \\ \textrm{Diagonal:}\:h=\sqrt{\left(5.0\:cm\right)^2+\left(5.0\:cm\right)^2}=7.1\:cm \\ \textrm{Angle:}\:\theta=\tan^{-1}\left(\frac{5.0\:cm}{5.0\:cm}\right)=45^{\circ} {/eq}


Equations:

{eq}\vec{E}=\frac{k\left\|{Q}\right\|}{r^2}\left<{\cos\theta;\:\sin\theta}\right> \\ {/eq}


Part a:

{eq}\begin{align*} \vec{E_1}&=\frac{k\left\|{Q}\right\|}{r^2}\left<{\cos\left(180-45\right)^{\circ};\:\sin\left(180-45\right)^{\circ}}\right> \\ \\ \vec{E_1}&=\frac{9\times 10^{9}\:\frac{Nm^2}{C^2}\left\|{+11\times 10^{-9}\:C}\right\|}{\left(7.1\times 10^{-2}\:m\right)^2}\left<{\cos135^{\circ};\:\sin135^{\circ}}\right> \\ \\ \vec{E_1}&=\left<{-13.9\times 10^{3}\:\frac{N}{C};\:13.9\times 10^{3}\:\frac{N}{C}}\right> \\ \\ \\ \\ \end{align*} {/eq}


Part b:

{eq}\begin{align*} \vec{E_2}&=\frac{k\left\|{Q}\right\|}{r^2}\left<{\cos\left(180+45\right)^{\circ};\:\sin\left(180+45\right)^{\circ}}\right> \\ \\ \vec{E_2}&=\frac{9\times 10^{9}\:\frac{Nm^2}{C^2}\left\|{+11\times 10^{-9}\:C}\right\|}{\left(7.1\times 10^{-2}\:m\right)^2}\left<{\cos225^{\circ};\:\sin225^{\circ}}\right> \\ \\ \vec{E_2}&=\left<{-13.9\times 10^{3}\:\frac{N}{C};\:-13.9\times 10^{3}\:\frac{N}{C}}\right> \end{align*} {/eq}


Part c:


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Electric Fields Practice Problems

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Chapter 17 / Lesson 8
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In this lesson, you will be introduced to electric fields so that you can practice calculating single fields, multiple fields, and electric fields in charged spheres. You'll also learn how Faraday cages work.


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