A 4.70 nC point charge is placed at the centre of a hollow metal sphere that has an inner radius 4.70 cm and an outer radius 17.6 cm. The metal sphere itself is charged to 8.40 nC.

a)What is the magnitude of the electric field at a distance of 1.60 cm from the centre?

b)What is the magnitude of the electric field at a distance of 11.2 cm from the centre?

c)What is the magnitude of the electric field at a distance 29.7 cm from the centre?

d)How much charge is on the inside surface of the hollow sphere?

e)How much charge is on the outside surface of the hollow sphere?

NOTE: Please i'm not asking for the final answer... Just a guideline on how to solve these questions... Thanks in advance for your help!!:-)

a) Zero. No field in a charged sphere.

b) Still zero
c) Now you can use your field equation. The field is a vector so you can sum the influence of the point charge and shell. Note r is different for each.
d)Again, none
e) all of it

To solve these questions, we can use the principle of superposition. The electric field at a point due to multiple charges is equal to the vector sum of the individual electric fields from each charge.

The electric field due to a point charge is given by Coulomb's law:

E = k * (q / r^2),

where E is the electric field, k is Coulomb's constant (8.99 x 10^9 Nm^2/C^2), q is the charge, and r is the distance from the charge.

a) To find the magnitude of the electric field at a distance of 1.60 cm from the centre, we need to consider the electric field due to the point charge at the centre and the electric field due to the charged metal sphere. Since the charge of the point charge and the charged metal sphere are the same (+4.70 nC), we can add their electric fields vectorially.

b) To find the magnitude of the electric field at a distance of 11.2 cm from the centre, we need to consider the electric field due to the charged metal sphere only. The electric field at this distance will be the electric field due to the charged metal sphere, taking into account its charge (+8.40 nC).

c) To find the magnitude of the electric field at a distance of 29.7 cm from the centre, we need to consider the electric field due to the charged metal sphere only. The electric field at this distance will be the electric field due to the charged metal sphere, taking into account its charge (+8.40 nC).

d) To find the charge on the inside surface of the hollow sphere, we need to consider the charge of the charged metal sphere and subtract the charge of the point charge at the centre.

e) To find the charge on the outside surface of the hollow sphere, we need to consider the charge of the charged metal sphere.

Remember to convert the charges from nanocoulombs (nC) to coulombs (C) when performing calculations.