Two effectively infinite and parallel sheets of charge are 6.00 cm apart. Sheet 1 carries a uniform surface charge density of -6.80 μC/m2 while Sheet 2, which is to the right of sheet 1, carries -12.4 μC/m2.
Find the magnitude and direction of the net electric field these sheets produce at a point (a) 2.00 cm to the right of sheet 1; (b) 2.00 cm to the left of sheet 1; (c) 2.00 cm to the right of sheet 2.
To find the magnitude and direction of the net electric field at various points, we can use the principle of superposition. The electric field produced by each sheet of charge can be calculated individually, and then the results can be added together to find the total electric field.
(a) To find the electric field at a point 2.00 cm to the right of sheet 1:
1. First, we find the electric field produced by sheet 1 at this point.
- We can use the formula for the electric field due to a sheet of charge:
Electric Field = (σ / 2ε₀), where σ is the surface charge density and ε₀ is the permittivity of free space.
- Plugging in the values, we have:
Electric Field due to sheet 1 = (-6.80 μC/m2 / 2ε₀)
2. Next, we find the electric field produced by sheet 2 at this point.
- Since sheet 2 is to the right of sheet 1, the electric field due to sheet 2 is zero at this point. This is because the electric field from sheet 2 is canceled out by the electric field from sheet 1.
3. Finally, we add the electric fields from step 1 and step 2 to find the net electric field at the point:
Net Electric Field = Electric Field due to sheet 1 + Electric Field due to sheet 2
(b) To find the electric field at a point 2.00 cm to the left of sheet 1:
- We can follow the same steps as in part (a) but reverse the direction of the electric field from sheet 1 since we are now on the opposite side.
(c) To find the electric field at a point 2.00 cm to the right of sheet 2:
- We can follow the same steps as in part (a) but only calculate the electric field due to sheet 2 since sheet 1 is not affecting this point.
By following these steps, you will be able to find the magnitude and direction of the net electric field at each of the given points.