Electricity and Magnetism

# Coulomb's law

Four equal charges, $$q = 6 \times 10^{-6} \text{ C }$$ , are situated at the corners of a square as shown in the above diagram. What is the net force (in Newtons) on the test charge $$Q = 9 \times 10^{-6} \text{ C }$$ at the center?

Let $$\pi \approx 3$$ and the permitivity of free space $$\epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2}$$

Two charges Q=+1 mC are placed along the x-axis at x=-2 meters and x=2 meters. The charges are fixed in space. A third charge, which is free to move and has charge q=-0.1 mC and mass m=1g, is placed along the y-axis at y=0.01 meters and released. How long does it take in seconds for the charge to come back to y=0.01?

Details and assumptions

• $$k=(4 \pi \epsilon_0)^{-1}= 9 \times 10^9~Nm^2/C^2$$

If the magnitude of the electric field a distance $$z = 9 \text{ m}$$ above the midpoint between two equal charges, $$q = 25 \times 10^{-12} \text{ C }$$, a distance $$2d =24 \text{ m}$$ apart can be expressed as $$E = \frac{a}{b} \text{ N/C},$$ where $$a$$ and $$b$$ are coprime positive integers, what is the value of $$a+b?$$

Let $$\pi \approx 3$$ and the permitivity of free space $$\epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2}$$

A test charge $$Q = 5 \times 10^{-6} \text{ C }$$ is placed by a single point charge $$q = 7 \times 10^{-6} \text{ C }$$ which is at rest at a distance of $$r = 4 \text{ m }$$ away. If the force can be expressed as $$F = \frac{a}{b} \text{ N},$$ where $$a$$ and $$b$$ are coprime positive integers, what is the value of $$a+b?$$

Let $$\pi \approx 3$$ and the permitivity of free space $$\epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2}$$

If the magnitude of the electric field at a distance of $$r = 3 \text{ m}$$ from the point charge $$Q = 9 \times 10^{-12} \text{ C }$$ can be expressed as $$E = \frac{a}{b} \text{ N/C},$$ where $$a$$ and $$b$$ are coprime positive integers, what is the value of $$a+b?$$

Let $$\pi \approx 3$$ and the permitivity of free space $$\epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2}$$

×