Question

Consider the charges 𝑞₁=2.5 𝜇𝐶 and 𝑞₂=-2 𝜇𝐶 located at (𝑥₁,𝑦₁,𝑧₁)=(1,−2,4) 𝑚 and (𝑥₂,𝑦₂,𝑧₂)=(2,-1, 3) 𝑚, respectively. Assume the charges are in the air.

a.) Determine the force exerted by charge 𝑞₂ on 𝑞₁

b.) Calculate the magnitude of the force on part a.

c.) Find the electric field at (𝑥₁,𝑦₁,𝑧₁) induced by charge 𝑞₂

d.) Determine the force exerted on charge 𝑞₁ due to the electric field of charge 𝑞₂.

Answer 1

a) Determine the force exerted by charge 𝑞₂ on 𝑞₁:

$$F=k\frac{q_1q_2}{r^2}$$

b) Calculate the magnitude of the force on part a.

$$F=9·10^9\frac{2.5·10^{-6}·2·10^{-6}}{(2-1)^2+(-1-(-2))^2+(3-4)^2}=0.015\text{ N}.$$

c) Find the electric field at (𝑥₁,𝑦₁,𝑧₁) induced by charge 𝑞₂

$$E=\frac{F}{q_1}=k\frac{q_1}{r^2}=7500\text{ V/m}.$$

d) Determine the force exerted on charge 𝑞₁ due to the electric field of charge 𝑞₂.

$$F=Eq_1=k\frac{q_1q_2}{r^2}=0.015\text{ N}.$$