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## Electric Flux

Electric flux connects the geometry of conductors to the fields they generate. Learn this powerful tool and shortcut your way to the electric field of symmetrical arrangements like wires and sheets.

# Field Lines and Field Strength

Four charged particles are held on the same plane, as shown in the above figure. The respective charges of the particles are $$q_1=q_2=+5.0 \,\mu\text{C},$$ $$q_3=+4.0 \,\mu\text{C},$$ and $$q_4=-16.0 \,\mu\text{C},$$ and the distance $$d$$ in the figure is $$8.0 \text{ mm}.$$ What is the magnitude of the net electric field at point $$P$$ due to the four particles?

The value of electrostatic constant is $$\displaystyle k=\frac{1}{4\pi\varepsilon_0}=8.99 \times 10^9 \text{ N}\cdot\text{m}^2\text{/C}^2.$$

Four particles are at the corners of a square with side length $$a=5.00\text{ cm},$$ as shown in the above figure. The respective charges of the particles are $$q_1=+12.0\text{ nC},$$ $$q_2=-24.0\text{ nC},$$ $$q_3=+24.0\text{ nC},$$ and $$q_4=-12.0\text{ nC}.$$ What are the magnitude and direction of the net electric field at the center of the square?

The value of electrostatic constant is $$\displaystyle k=\frac{1}{4\pi\varepsilon_0}=8.99 \times 10^9 \text{ N}\cdot\text{m}^2\text{/C}^2.$$

In the above figure, the separation of electric field lines on the left is twice the separation of those on the right. If the magnitude of the field at position A is $$70\text{ N/C},$$ what is the magnitude of the field at position B?

Three charged particles are held on the $$xy$$-plane, as shown in the above figure. The distance denoted $$d$$ in the figure is $$d=6.00\,\mu\text{m}.$$ If the respective charges of the particles are $$q_1=q_2=+4e$$ and $$q_3=+8e,$$ what is the magnitude of the net electric field at point $$P$$ due to the three charged particles?

The value of electrostatic constant is $$\displaystyle k=\frac{1}{4\pi\varepsilon_0}=8.99 \times 10^9 \text{ N}\cdot\text{m}^2\text{/C}^2$$ and the elementary charge is $$e=1.60 \times 10^{-19}\text{ C}.$$

The figure above portrays the electric field produced by two positive-charged particles. Which of the following correctly lists the points A, B, C, and D in order of increasing electric field strength?

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