A conducting sphere that carries a total charge of -6 micro-coulomb is placed at the center of a conducting spherical shell that carries a total charge of +1 micro-coulomb. The conductors are in elecctrostatic equilibrium. determine the charge on the OUTER SURFACE of the shell. (hint: sketch a field line diagram)

To determine the charge on the outer surface of the conducting shell, we need to understand the concept of electric field lines and how charges distribute in conductors in electrostatic equilibrium.

First, let's analyze the scenario described in the question. We have a conducting sphere at the center, carrying a charge of -6 μC, and a conducting spherical shell surrounding it with a total charge of +1 μC.

In electrostatic equilibrium, charges distribute themselves on conductors in a way that the electric field inside the conductor is zero. Therefore, we can conclude that the charge on the inner surface of the conducting shell will be -6 μC (opposite in sign to the charge on the sphere) to ensure zero electric field inside the shell.

Now, let's consider the outer surface of the shell. Since the electric field inside the conductor is zero, there will be no electric field lines originating or terminating on the outer surface of the shell. This means that the electric field due to the charges on the inner surface and the charges on the sphere cancel each other out, resulting in no electric field outside the conductor.

Since the electric field outside the conductor is zero, we can assume that the total charge distributed on the shell's outer surface is zero. As a result, the charge on the outer surface of the conducting shell is also zero.

In conclusion, the charge on the outer surface of the shell is zero.

To determine the charge on the outer surface of the shell, we need to consider the principle of electrostatic equilibrium. In this scenario, electrostatic equilibrium means that the electric field inside the conductors is zero.

Let's break down the steps to solve the problem:

Step 1: Understand the concept
- The conducting sphere and the conducting shell are both electrically conductive, meaning they have free charges that can move.
- When placed in contact, charges from the conductors will redistribute themselves until the electric field inside both conductors is zero.
- Conceptually, the charges move in such a way that the net electric field within both conductors cancels out.

Step 2: Determine the charge redistribution
- The conducting sphere carries a total charge of -6 micro-coulomb.
- The conducting shell carries a total charge of +1 micro-coulomb.
- The charges will redistribute themselves until the net electric field inside both conductors is zero.

Step 3: Analyze charge distribution
- Since the charge on the conducting shell is positive, the excess positive charge will move to the outer surface.
- The negative charge on the conducting sphere will repel the positive charge on the conducting shell, causing negative charge to accumulate on the inner surface of the shell facing the sphere.
- At the same time, the accumulated negative charge on the inner surface of the conducting shell will repel some negative charge from the conducting sphere to the outer surface of the shell.
- The negative charge on the outer surface of the shell will be distributed in such a way that it cancels out the positive charge on the inner surface due to electrostatic equilibrium.

Step 4: Determine the charge on the outer surface of the shell
- We know that for electrostatic equilibrium, the electric field inside the conductors must be zero.
- For this to happen, the charges on the outer surface of the shell must exactly cancel out the charges on the inner surface.
- Since the inner surface of the shell carries a charge of +1 micro-coulomb and the charge on the conducting sphere is -6 micro-coulomb, the charge on the outer surface must be the sum of the two charges: -6 micro-coulomb + 1 micro-coulomb = -5 micro-coulomb.

Therefore, the charge on the outer surface of the shell is -5 micro-coulomb.

"Electrostatic equilibrium" means the charges are not moving around. There is zero E-field inside the conductors.

The -6uC charge of the conducting sphere resides entirely at its surface, evenly distributed.

Gauss' law and the equilibrium requirement tells you that there can be no net charge inside a conducting spherical surface that passes between the inner and outer surfaces of the outer shell. That means there must be +6uC on the inner surface.

In order to have a net charge of 1 uC, there must be a charge of -5uC on the outer surface of the conducting shell.