Question

Two parallel, infinite, nonconducting plates are \(10.0 \mathrm{~cm}\) apart and have charge distributions of \(+1.00 \mu \mathrm{C} / \mathrm{m}^{2}\) and \(-1.00 \mu \mathrm{C} / \mathrm{m}^{2} .\) What is the force on an electron in the space between the plates? What is the force on an electron located outside the two plates near the surface of one of the two plates?

Short answer

Answer: The force on an electron between the plates is approximately -3.616 × 10^{-14} N, directed towards the positive plate. The force on an electron outside the plates near the surface is 0 N.

Step-by-step solution

Calculate the electric field due to the positive charge distribution on the plate

E1 = (1.00 * 10^{-6} C/m²)/(8.85 * 10^{-12} C²/N·m²) = 113000 N/C

Calculate the electric field due to the negative charge distribution on the plate

E2 = (1.00 * 10^{-6} C/m²)/(8.85 * 10^{-12} C²/N·m²) = - 113000 N/C

Calculate the total electric field between the plates

E_total = E1 + E2 = 113000 N/C + (- 113000 N/C) = 226000 N/C Step 2: Finding the force on an electron between the plates

Calculate the force on an electron in the electric field

F = qE = (-1.6 * 10^{-19} C)(226000 N/C) = -3.616 * 10^{-14} N Step 3: Finding the electric field outside the plates

Calculate the electric field due to the positive and negative charge distributions at the same point outside the plates

Using the principle of superposition, the electric field from both the positive and negative charge distributions are equal and opposite. The sum of these fields is E_outside = 0 N/C. Step 4: Finding the force on an electron outside the plates

Calculate the force on an electron in the electric field outside the plates

Since the electric field outside the plates is 0 N/C, the force on an electron is F_outside = qE_outside = (-1.6 * 10^{-19} C)(0 N/C) = 0 N The force on an electron in the space between the plates is approximately -3.616 × 10^{-14} N (directed towards the positive plate), and the force on an electron located outside the two plates near the surface of one of the two plates is 0 N.