A solid nonconducting sphere of radius 13 cm has a positive charge 9.8 × 10-8 C spread uniformly throughout its volume. The electric field at a point within the sphere at a radius 5.0 cm has a magnitude of
To find the electric field at a point within the sphere, we can use Gauss's Law. Gauss's Law states that the electric flux through a closed surface is directly proportional to the charged enclosed by the surface.
The formula to calculate the electric field inside a uniformly charged sphere is given by:
E = (1 / (4πε₀)) * (Q / R³) * r
Where:
E is the electric field at the point within the sphere
ε₀ is the permittivity of free space (8.854 × 10⁻¹² C²/(N*m²))
Q is the charge enclosed by the Gaussian surface (charge of the sphere)
R is the radius of the sphere
r is the distance from the center of the sphere to the point within the sphere
Given:
Charge of the sphere, Q = 9.8 × 10⁻⁸ C
Radius of the sphere, R = 13 cm = 0.13 m
Distance from the center to the point within the sphere, r = 5.0 cm = 0.05 m
Plugging in the values into the formula:
E = (1 / (4πε₀)) * (Q / R³) * r
E = (1 / (4π * (8.854 × 10⁻¹²))) * ((9.8 × 10⁻⁸) / (0.13)³) * 0.05
Calculating this expression will give you the magnitude of the electric field at the given point within the sphere.