Consider a thin spherical shell of radius 20.2cm with a total charge of 3.3μC distributed uniformly on its surface.
a) Find the electric field, in N/C, at a radius of 15.6cm from the center of the charge distribution.
b) Find the electric field, in N/C, at a radius of 27.3cm from the center of the charge distribution.
To find the electric field at a certain radius from a charged spherical shell, you can use the formula for the electric field due to a uniformly charged spherical shell:
E = k * Q * r / R^3
where:
- E is the electric field at the given radius,
- k is the electrostatic constant (k ≈ 9 × 10^9 Nm^2/C^2),
- Q is the total charge on the spherical shell,
- r is the distance from the center of the shell to the point where you want to find the electric field,
- R is the radius of the spherical shell.
a) To find the electric field at a radius of 15.6 cm from the center of the charge distribution (r = 15.6 cm = 0.156 m), we can substitute the values into the formula:
E = (9 × 10^9 Nm^2/C^2) * (3.3 × 10^(-6) C) * (0.156 m) / (0.202 m)^3
Calculating this expression will give you the electric field at a radius of 15.6 cm from the center of the charge distribution.
b) To find the electric field at a radius of 27.3 cm from the center of the charge distribution (r = 27.3 cm = 0.273 m), we can again substitute the values into the formula:
E = (9 × 10^9 Nm^2/C^2) * (3.3 × 10^(-6) C) * (0.273 m) / (0.202 m)^3
Calculating this expression will give you the electric field at a radius of 27.3 cm from the center of the charge distribution.