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# Charges and Their Interactions

The motion of charged matter underlies many things we enjoy like phones and plasma globes. It also puts a permanent end to the enjoyment of some 6,000 people per year, as fatal lightning strikes.

# Lorentz force (Electric fields)

An electron floats at rest above a sheet of charge with uniform charge density $$\sigma$$. What is $$\sigma$$ in $$\mbox{C/m}^2$$?

Details and assumptions

• The mass of the electron is $$9.1 \times 10^{-31}~\mbox{kg}$$.
• The electric charge on the electron is $$-1.6 \times 10^{-19}~\mbox{C}$$.
• The acceleration due to gravity is $$-9.8~\mbox{m/s}^2$$.
• The vacuum permittivity is $$\epsilon_0=8.85 \times 10^{-12}~\mbox{F/m}$$.

A point particle with mass $$m = 2 \text{ kg}$$ and charge $$Q = 33 \text{ C }$$ is shot with speed $$v = 8 \text{ m/s}$$ at an angle of $$\theta = 30^o$$ with the ground. There is an electric field $$\vec{E} = -22 \hat{y}\text{ N/C}$$ heading perpendicularly to the ground. When the particle falls to the ground, the distance from the original point can be expressed as $$R = \frac{a}{b} \text{ m},$$ where $$a$$ and $$b$$ are coprime positive integers, what is the value of $$a+b?$$

Assume that $$\sqrt{3} = 1.5$$

A point particle with mass $$m = 1\text{ kg}$$ and charge $$Q = 8 \text{ C }$$ is shot with speed $$v = 3 \text{ m/s}$$ at an angle of $$\theta = 30^\circ$$ with the ground. There is an electric field $$\vec{E} = 3\hat{x} - 6\hat{y} \text{ N/C},$$ as shown in the above diagram. When the particle falls to the ground, the distance from the original point can be expressed as $$R = \frac{a}{b} \text{ m},$$ where $$a$$ and $$b$$ are coprime positive integers. What is the value of $$a+b?$$

Assume that $$\sqrt{3} = 1.5 .$$

A point particle with mass $$m = 6 \text{ kg}$$ and charge $$Q = 6 \text{ C }$$ is shot with initial speed $$v(0) = 6 \text{ m/s}$$ at an angle of $$\theta = 60^\circ$$ with the ground. There is an electric field $$\vec{E} = -6 \hat{y}\text{ N/C},$$ as shown in the above diagram. When $$t = \frac{3}{4}\text{ s},$$ what is the speed of the particle ?

Assume that $$\sqrt{3} = 1.5$$

A point particle with mass $$m = 1 \text{ kg}$$ and charge $$Q = 9 \text{ C }$$ is shot with speed $$v = 6 \text{ m/s}$$ at an angle of $$\theta = 30^o$$ with the ground. There is an electric field $$\vec{E} = -9 \hat{y}\text{ N/C},$$ as shown in the above diagram. If the maximum height can be expressed as $$H = \frac{a}{b} \text{ m},$$ where $$a$$ and $$b$$ are coprime positive integers, what is the value of $$a+b?$$

There is no gravitational field present.

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