(455) HL Hollow conducting sphere [IB Physics HL]

Hollow Conducting Sphere

General Concepts

• Conductivity: The sphere is made of a metal that conducts electricity well and is positively charged.

• Electric Field Lines: Electric field lines extend outwards from the sphere, indicating the direction a positive test charge would move.

Equations to Remember

• Electric Field Strength: ( E = -\frac{\Delta V_e}{\Delta R} )

• Electric Potential: ( V_e = \frac{kQ}{R} )

Electric Field and Potential Outside the Sphere

• Behavior of Electric Field and Potential:

  • Both the electric field strength and electric potential decrease with increasing distance from the sphere, behaving as ( \frac{1}{R} ).

Electric Field and Potential Inside the Sphere

• Charge Distribution: All charge resides on the outer surface of the sphere.

• Electric Field Inside:

  • Since charges on the surface cancel out, the electric field strength inside the sphere is zero (E = 0).

• Electric Potential Inside:

  • With ( E = 0 ) and no change in potential (( \Delta V_e = 0 )), it implies that the electric potential inside is constant.

  • This means no work is needed to move within the sphere's interior.

Summary of Graphs

• Sketching Electric Field and Potential:

  • Inside the Sphere: Electric field is zero, electric potential is constant.

  • Outside the Sphere: Electric field and potential decrease following the ( \frac{1}{R} ) relationship, starting from a positive value down to zero as distance increases.