Question

Consider two conducting spheres. The outer sphere is hollow and initially has charge $-7Q$ on it. The inner sphere is solid and has a charge $+2Q$ on it. We now connect the outer sphere to ground with a wire and then disconnect it. How much total charge will be on the outer sphere?

Answer 1

Hint: We know that the charges are the most elementary particles which are responsible for the flow of current. We also know that when the charge carrier is grounded, then the charges are transferred to the ground.

Complete step by step solution:
Given that there are two conducting spheres, such that the outer sphere is hollow and initially has charge $-7Q$ on it and the inner sphere is solid and has a charge $+2Q$ on it. Let us consider the same in the form of the diagram as shown below,

We know that the charges have an ability to induce opposite charges on the other side of the carrier. Here, since the internal solid sphere carries a charge $+2Q$, we can say that it induces a charge of $-2Q$ on the interior of the outer hollow sphere. This new induced charge, again induces a charge of $+2Q$ on the outer surface, then the total charge on the outer surface is given as $-7Q+2Q=5Q$.
Since the outer surface is grounded, we can say that the net charge on the outer surface is lost.
But since, the interior also has some charge, that is $-2Q$, then the total charge on the inner surface of the outer ring after it is grounded is given as $-2Q$, while the total charge on the outer surface of the outer ring after grounding is $0\;Q$

Additional Information: We know that the electric force due to a pair of charges is given by the coulomb's law. An electric field can be produced by a time-varying electric field or an electrical charge. These can be either attracting or repelling in nature.

Note: Electric charge can either be positive or negative. Also, moving electric charge can produce current. A few other properties of electrical charge are electric force, electric field and electric potential.