Question

A point charge of -3.00 μC is located in the center of a spherical cavity of radius 6.50 cm inside an insulating spherical charged solid. The charge density in the solid is 7.35 × 10⁻⁴ C/m³. What is the total charge enclosed by the solid?

1) Cannot be determined
2) 0 C
3) -3.00 μC
4) 3.00 μC

Answer 1

The total charge enclosed by the solid is calculated by finding the volume of the solid material excluding the spherical cavity, and multiplying it with the charge density, then adding the point charge placed in the cavity.

Step-by-step explanation:

The student asked about the total charge enclosed by a solid with a spherical cavity at the center that houses a point charge of -3.00 µC, while the solid itself has a charge density of 7.35 × 10⁻⁴ C/m³. To find the total charge enclosed by the solid, we need to calculate the charge contributed by the volume of the solid excluding the cavity and add the charge of the point charge in the cavity.

The charge in the solid material itself can be found by calculating the volume of the solid and multiplying by the charge density. Volume of a solid sphere is given by ⅓πr³, where r is the radius of the sphere. However, we subtract the volume of the cavity (also calculated using ⅓πr³ for its radius), as it does not contain the solid material. Then, multiply the charge density (7.35 × 10⁻⁴ C/m³) by the solid's volume excluding the cavity to find the charge.

Finally, we add the point charge in the cavity (-3.00 µC) to the charge calculated from the solid's volume to obtain the total charge enclosed by the solid.