The electric field at a distance of 0.150 m from the surface of a solid insulating sphere with radius 0.367 m is 1720 N/C .
Assuming the sphere's charge is uniformly distributed, what is the charge density inside it?
Calculate the electric field inside the sphere at a distance of 0.215 m from the center.
To find the charge density inside the sphere, we need to use the formula:
Charge density (ρ) = Total charge (Q) / Volume (V)
The total charge Q of the sphere can be found using the formula for electric field:
Electric field (E) = k * Q / r^2
Where E is the electric field, k is Coulomb's constant (8.99 * 10^9 N m^2/C^2), Q is the total charge, and r is the distance from the center of the sphere.
Rearranging the equation, we get:
Q = E * r^2 / k
Substituting the values given in the problem:
Q = (1720 N/C) * (0.150 m)^2 / (8.99 * 10^9 N m^2/C^2)
Simplifying:
Q = 1.110 * 10^-9 C
Now, to find the volume of the sphere, we use the formula:
Volume (V) = (4/3) * π * r^3
Substituting the given radius:
V = (4/3) * π * (0.367 m)^3
Simplifying:
V = 0.181 m^3
Finally, we can calculate the charge density:
ρ = Q / V
Substituting the values:
ρ = (1.110 * 10^-9 C) / (0.181 m^3)
Simplifying:
ρ = 6.124 * 10^-9 C/m^3
So, the charge density inside the sphere is 6.124 * 10^-9 C/m^3.
To calculate the electric field inside the sphere at a distance of 0.215 m from the center, we can use the same formula:
Electric field (E) = k * Q / r^2
Substituting the values:
E = (8.99 * 10^9 N m^2/C^2) * (1.110 * 10^-9 C) / (0.215 m)^2
Simplifying:
E = 6307 N/C
Therefore, the electric field inside the sphere at a distance of 0.215 m from the center is 6307 N/C.