A hollow metal sphere has 6 cm inner and 8cm outer radii. The surface charge densities on the exterior surface is +100 nC/m2 and -100 nC/m2 on the interior surface. (1) What are the strength and direction of the electric field at points 4cm, 8cm and 12cm from the center

Answer:Outer Electric Field is 11250 N/C.Inner Electric Field is -10000 N/C.Step-by-step explanation:First of all, we need to read carefully and analyse the problem. As you can see, is an electrical subject, and it's given surface charge densities and radius. So, to calculate electric fields, we need to find the proper equation to do so: [tex]E=k\frac{q}{r^{2} }[/tex]; as you can see, first we need to find the charges.We can find all charges using the surface charge densities, because it has the next relation: [tex]p=\frac{q}{A}[/tex]; which indicates that charge density is the amount of charge per area. But, there's a problem, we don't have areas, so we have to calculate them first with this relation: [tex]S=4\pi r^{2}[/tex]; which gives us the surface of a sphere.The inner surface: [tex]Si=4\pi (0.06m)^{2} = 0.04 m^{2}[/tex]The outer surface: [tex]S=4\pi (0.08m)^{2}=0.08m^{2}[/tex]Now we can calculate the charges,Inner charge: [tex]Qi=pA=(-100\frac{nC}{m^{2} } )(0.04m^{2} )=-4nC[/tex]Outer charge: [tex]Qo=pA=100\frac{nC}{m^{2} } )(0.08m^{2} )=8nC[/tex]Then, we are able to calculate both fields:Inner field: [tex]Ei=k\frac{Qi}{r^{2} }=9x10^{9} \frac{Nm^{2} }{C^{2} }\frac{-4x10^{-9} }{0.06m^{2} }=-10000\frac{N}{C}[/tex]Outer field:  [tex]Eo=k\frac{Qo}{r^{2} }=9x10^{9} \frac{Nm^{2} }{C^{2} }\frac{8x10^{-9} }{0.08m^{2} }=11250\frac{N}{C}[/tex]The directions that field have is opposite each other, the inner one has an inside direction, and the outer electric field has an outside direction.