Electricity and Magnetism

Charges and Their Interactions

Coulomb's law

         

Four equal charges, q=6×10−6 C  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=9×10−6 C  Q = 9 \times 10^{-6} \text{ C } at the center?

Let π≈3 \pi \approx 3 and the permitivity of free space ϵ0≈9×10−12C2N*m2 \epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2}

by Brilliant Staff

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=(4πϵ0)−1=9×109 Nm2/C2k=(4 \pi \epsilon_0)^{-1}= 9 \times 10^9~Nm^2/C^2
by Brilliant Staff

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

Let π≈3 \pi \approx 3 and the permitivity of free space ϵ0≈9×10−12C2N*m2 \epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2}

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by Brilliant Staff

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

Let π≈3 \pi \approx 3 and the permitivity of free space ϵ0≈9×10−12C2N*m2 \epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2}

Show explanation
View wiki
by Brilliant Staff

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

Let π≈3 \pi \approx 3 and the permitivity of free space ϵ0≈9×10−12C2N*m2 \epsilon_0 \approx 9\times 10^{-12} \frac{\text{C}^2}{\text{N*m}^2}

Show explanation
View wiki
by Brilliant Staff
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