Answer :
Final Answer
The magnitude of the electric field due to the charge distribution at a distance of 8.00 cm from the center of the sphere is 990 N/C. This indicates that the electric field remains constant at this distance due to the uniform distribution of charge within the insulating sphere.
The correct option is a) The magnitude of the electric field due to the charge distribution at a distance of 8.00 cm from the center of the sphere is 990 N/C.
Explanation
The electric field (E) at a distance [tex](r)[/tex] from the center of a uniformly charged insulating sphere can be calculated using the formula[tex]\(E = \frac{{kq}}{{r^2}}\),[/tex] where [tex]\(k\)[/tex] is Coulomb's constant. Here, [tex]\(r\)[/tex] is given as 8.00 cm. Substituting the given values into the formula, we have [tex]\(990 = \frac{{kq}}{{(0.08)^2}}\).[/tex]Solving for [tex]\(q\),[/tex]we find the value of [tex]\(q\)[/tex] to be [tex]\(1.58 \times 10^{-8}\) C.[/tex]
Uniform distribution of charge within the sphere implies that the charge is evenly spread throughout the volume. Therefore, the electric field magnitude remains constant at any distance outside the sphere. Thus, at a distance of 8.00 cm from the center, the magnitude of the electric field is 990 N/C.
The answer provides the direct result of the electric field magnitude at a specific distance from the center of the sphere, fulfilling the requirements of the question. It is crucial to understand the relationship between electric field and distance from a uniformly charged sphere to determine the correct answer.
The correct option is a) The magnitude of the electric field due to the charge distribution at a distance of 8.00 cm from the center of the sphere is 990 N/C.
