To find the charge on the outer surface of the conducting spherical shell, we need to apply the principles of electrostatics, particularly Gauss's law and the behavior of conductors in electrostatic equilibrium. Let's break this down step by step.
Understanding the System
We have a solid conducting sphere with a radius of 0.7 cm and a charge of -7.3 pC. Surrounding this sphere is a conducting spherical shell with an inner radius of 2.8 cm and an outer radius of 5 cm, which has a total charge of +27.9 pC. The charges on the inner and outer surfaces of the shell will be denoted as Qinner and Qouter, respectively.
Applying Gauss's Law
According to Gauss's law, the electric field inside a conductor in electrostatic equilibrium is zero. This means that any excess charge resides on the outer surface of the conductor. The charge distribution will adjust itself so that the electric field inside the conducting material is zero.
Charge Distribution
- The charge on the solid sphere is -7.3 pC.
- To maintain electrostatic equilibrium, the inner surface of the shell must have a charge that exactly cancels the electric field produced by the solid sphere. Therefore, the charge on the inner surface of the shell, Qinner, will be +7.3 pC.
- Now, since the total charge on the shell is +27.9 pC, we can find the charge on the outer surface of the shell.
Calculating Qouter
The total charge on the shell is the sum of the charges on its inner and outer surfaces:
Qtotal = Qinner + Qouter
Substituting the known values:
27.9 pC = 7.3 pC + Qouter
To find Qouter, we rearrange the equation:
Qouter = 27.9 pC - 7.3 pC
Calculating this gives:
Qouter = 20.6 pC
Final Result
Thus, the charge on the outer surface of the conducting spherical shell, Qouter, is 20.6 pC.
