Electricity and Magnetism

Charges and Their Interactions

Lorentz force (Electric fields)

         

An electron floats at rest above a sheet of charge with uniform charge density σ\sigma. What is σ\sigma in C/m2\mbox{C/m}^2?

Details and assumptions

  • The mass of the electron is 9.1×1031 kg9.1 \times 10^{-31}~\mbox{kg}.
  • The electric charge on the electron is 1.6×1019 C-1.6 \times 10^{-19}~\mbox{C}.
  • The acceleration due to gravity is 9.8 m/s2-9.8~\mbox{m/s}^2.
  • The vacuum permittivity is ϵ0=8.85×1012 F/m\epsilon_0=8.85 \times 10^{-12}~\mbox{F/m}.
  • If your answer is 1.23×104\num{1.23e-4} submit 1.23E-4.

A point particle with mass m=2 kg m = 2 \text{ kg} and charge Q=33 C  Q = 33 \text{ C } is shot with speed v=8 m/s v = 8 \text{ m/s} at an angle of θ=30o\theta = 30^o with the ground. There is an electric field E=22y^ N/C \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=ab m, R = \frac{a}{b} \text{ m}, where aa and bb are coprime positive integers, what is the value of a+b?a+b?

Assume that 3=1.5\sqrt{3} = 1.5 and there is no gravitational field.

A point particle with mass m=1 kg m = 1\text{ kg} and charge Q=8 C  Q = 8 \text{ C } is shot with speed v=3 m/s v = 3 \text{ m/s} at an angle of θ=30\theta = 30^\circ with the ground. There is an electric field E=3x^6y^ N/C, \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=ab m, R = \frac{a}{b} \text{ m}, where aa and bb are coprime positive integers. What is the value of a+b?a+b?

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

A point particle with mass m=6 kg m = 6 \text{ kg} and charge Q=6 C  Q = 6 \text{ C } is shot with initial speed v(0)=6 m/s v(0) = 6 \text{ m/s} at an angle of θ=60\theta = 60^\circ with the ground. There is an electric field E=6y^ N/C, \vec{E} = -6 \hat{y}\text{ N/C}, as shown in the above diagram. When t=34 s,t = \frac{3}{4}\text{ s}, what is the speed of the particle ?

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

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

There is no gravitational field present.

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