Electricity and Magnetism
# Electric Flux

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 \(\displaystyle k=\frac{1}{4\pi\varepsilon_0}=8.99 \times 10^9 \text{ N}\cdot\text{m}^2\text{/C}^2.\)

**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 \(e=1.60 \times 10^{-19}\text{ C}.\)

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