A point charge of 5.5 µC is located at

the center of a spherical shell of radius 30 cm, which has a charge −5.5 µC uniformly distributed on its surface.

Given:
ke = 8.98755 × 10^9

Find the electric field for a point inside the shell a distance 12 cm from the center.

To find the electric field at a point inside the shell, you can use the principle of superposition. The electric field at that point is the vector sum of the electric fields due to the point charge at the center and the electric fields due to the uniformly distributed surface charge.

First, let's calculate the electric field due to the point charge at the center. The electric field due to a point charge at a distance r from it is given by Coulomb's law:

|E1| = ke * (|q1| / r^2)

where |q1| is the magnitude of the charge at the center and r is the distance from the point to the center. In this case, |q1| = 5.5 µC and r = 12 cm (0.12 m). Substituting these values into the equation, we get:

|E1| = (8.98755 × 10^9) * (5.5 × 10^-6 C) / (0.12 m)^2

Simplifying the expression, we find that the electric field due to the point charge is:

|E1| ≈ 0.203 N/C (newtons per coulomb)

Next, let's calculate the electric field due to the uniformly distributed surface charge on the spherical shell. The electric field at a point inside a conducting shell is zero. This means that the electric field due to the surface charge exactly cancels out the electric field due to the point charge at the center.

Therefore, the total electric field at a point inside the shell a distance 12 cm from the center is simply the electric field due to the point charge:

|Et| = |E1| ≈ 0.203 N/C (newtons per coulomb)

So, the electric field at a point inside the shell, 12 cm from the center, is approximately 0.203 N/C.