a) r > R:

1. 0 0 • Example: An insulating solid sphere of radius R has a uniform positive volume charge density and total charge Q. • Find the electric potential at a point outside the sphere (r > R). Take V = 0 at r = ¥. • Find the electric potential at a point inside the sphere (r < R). a) r > R: Outside the sphere we can determine the electric field using Gauss’s Law and we get the Electric field of a point charge Electric potential of a point charge

2. b) r < R: The electric field inside the sphere can be determined using Gauss’s Law Radial component of E Electric potential at the surface of the sphere To simplify expression

3. Electric potential due to a charged conductor We are now going to examine the electric potential of a conductor. In order to do so we must recall some important information about conductors. 1) What is the strength of the electric field inside a conductor? Zero – the electric field inside a conductor is always zero. 2) What is the strength and direction of the electric field outside of a conductor relative to the surface of the conductor? The electric field outside a conductor has a strength of s/e0 and is directed perpendicular to the surface (parallel to the area vector). 3) Where is all the excess charge located for a conductor? All excess charge is located on the surface of a conductor.

4. Let us now look at the electric potential of a conductor 1) If we have two points on the surface of a conductor, what is the potential difference between these two points? 0 E and ds are perpendicular as you move along the surface All points on the surface are electrically connected and therefore at the same electric potential. 2) What is the potential difference between a point inside the conductor and a point on the surface of the conductor? 0 The electric field is always zero inside a conductor All points on the surface are electrically connected to all point inside the conductor and therefore at the same electric potential. This means that all points anywhere on or in the conductor are all at the same potential !!

5. 3) How much work must be done to move a charge from one point on a conductor to another? 0 All points are at the same electric potential. Charges move freely in a conductor with no addition or loss of energy. What about a hollow conductor, what is the potential difference between two points on opposite sides of the cavity? The electric potential difference is still zero since all parts of the shell are still electrically connected. What is the electric field inside the cavity of a conductor? The net electric field is still zero inside the cavity of the conductor.

6. A solid spherical conductor is given a net nonzero charge. The electrostatic potential of the conductor is 1. largest at the center. 2. largest on the surface. 3. largest somewhere between center and surface. 4. constant throughout the volume.

7. Consider two isolated spherical conductors each having net charge Q. The spheres have radii aand b, where b> a. Which sphere has the higher potential? 1. the sphere of radius a 2. the sphere of radius b 3. They have the same potential. r = a or b

8. A conducting shell is primarily used as shielding. Anything that is inside the conductor is completely protected from any electric fields. • A conducting shell used for this purpose is often called a Faraday Cage. • Faraday cages are widely used to protect sensitive electronics from external influences. • Faraday cages can be made of solid conductors or a conducting mesh.