Calculate the electric potential of a sphere

[doktorwho]

Homework Statement

A metal sphere of radius $a=1cm$ is charged with $Q_a=1nC$. Around a sphere is placed a spherical shell of inner radius $b=2cm$ and outer radius $c=3cm$. The electrical potential of the shell in refenrence to a point in the infinity is $V=150V$. The spheres are in a vacuum. Calculate:
a) The electric potential of the inner sphere in reference to a point in the infinity
b) The total charge of the spherical shell

Homework Equations

3. The Attempt at a Solution [/B]
Im going to give you the results straight away so you can help me faster.
a) $600V$
b) $-0.5nC$
The first one i don't know how to start but the b) part i tried like this:
$V=\frac{Q}{4πξ_oR}$ where $R=C$ and got 0.5 but i don't get the $-$ part. I don't understand this problem..Can you help?

 

[I like Serena]

Homework Statement

A metal sphere of radius $a=1cm$ is charged with $Q_a=1nC$. Around a sphere is placed a spherical shell of inner radius $b=2cm$ and outer radius $c=3cm$. The electrical potential of the shell in refenrence to a point in the infinity is $V=150V$. The spheres are in a vacuum. Calculate:
a) The electric potential of the inner sphere in reference to a point in the infinity
b) The total charge of the spherical shell

Homework Equations

3. The Attempt at a Solution [/B]
Im going to give you the results straight away so you can help me faster.
a) $600V$
b) $-0.5nC$
The first one i don't know how to start but the b) part i tried like this:
$V=\frac{Q}{4πξ_oR}$ where $R=C$ and got 0.5 but i don't get the $-$ part. I don't understand this problem..Can you help?

Hi doktorwho!

For (b) you calculated the total enclosed charge, which is indeed +0.5 nC. Since the inner sphere carries 1 nC, the outer spherical shell must have -0.5 nC.

 

[hilbert2]

If the sphere and the shell are made of metal (a conductor), the electrical potential is constant in them. Use Gauss's law to determine the electric field at different radii between the sphere and the outer shell, and then integrate to find the potential difference between the sphere and the shell.

 

[doktorwho]

If the sphere and the shell are made of metal (a conductor), the electrical potential is constant in them. Use Gauss's law to determine the electric field at different radii between the sphere and the outer shell, and then integrate to find the potential difference between the sphere and the shell.

Can i do it like this?:
$V_a+∫Edl+V_c=V_{inner}$
Basically I am adding up the potential of the sphere at surface, the potential difference between point b and point a and the potential of the whole. Simply:
$V_b+V_c=V_{inner}$ where i use the respective Q-s. Since the potential of the $V_c=\frac{0.5}{4πε_or_c}$ and the $V_b$ is proportional to $V_c$ $V_b=2*\frac{3}{2}*V_c=450V$ i get 600. Is this correct thinking?

 

[hilbert2]

^ yes, that seems to be correct.