A hollow sphere has a uniform volume charge density of 4.61 nC/m3. The inner radius is a = 14.6 cm and the outer radius is b = 43.8 cm.
What is the magnitude of the electric field at 21.9 cm from the center of the sphere?
What is the magnitude of the electric field at 140. cm from the center of the sphere?
simple> Figure the total charge enclosed at the given r, then consider that a point charge at the center, E=kQ/r^2
Now on the volume of charge, remember it is a hollow, so figure the total volume of sphere, then subtract the empty volume, then multiply by charge density.
Look up Gauss' Law
To find the magnitude of the electric field at a certain distance from the center of the hollow sphere, we can use Gauss's Law. According to Gauss's Law, the electric field at a point is directly proportional to the net charge enclosed within a Gaussian surface surrounding that point.
1) Magnitude of electric field at 21.9 cm from the center:
To find the electric field at 21.9 cm from the center of the sphere, we need to calculate the net charge enclosed within a Gaussian surface of radius 21.9 cm.
a) Find the net charge enclosed within the Gaussian surface:
The net charge enclosed within the Gaussian surface is equal to the volume charge density multiplied by the volume of the Gaussian sphere. The volume of a hollow sphere can be calculated by subtracting the volume of the smaller sphere (with radius a) from the volume of the larger sphere (with radius b).
Volume of hollow sphere = (4/3) * π * b^3 - (4/3) * π * a^3
b) Calculate the electric field:
Once we have the net charge, we can use Gauss's Law to find the electric field. Gauss's Law states that the electric field is equal to the net charge enclosed divided by the permittivity of free space (ε0) multiplied by 4π (since the sphere has spherical symmetry).
Electric field = (net charge enclosed) / (4πε₀ * r²)
Substitute the values to find the magnitude of the electric field at 21.9 cm from the center.
2) Magnitude of electric field at 140 cm from the center:
We follow the same procedure as above but with a radius of 140 cm to find the magnitude of the electric field at that distance from the center.
Repeat the steps outlined above with r = 140 cm to calculate the magnitude of the electric field.