Charge Dynamics

 Let's consider a system of two objects, each with an initial charge Q1 and Q2, respectively. The total charge of the system is therefore:

Qtotal = Q1 + Q2

Now, let's say we want to change the charge on object 1 by a small amount ΔQ, while leaving the charge on object 2 unchanged. We can express the new charges as:

Q1' = Q1 + ΔQ Q2' = Q2

The new total charge of the system is:

Qtotal' = Q1' + Q2' = (Q1 + ΔQ) + Q2 = Q1 + Q2 + ΔQ

We can see that the total charge of the system has increased by ΔQ, which violates the principle of charge conservation.

To conserve the total charge of the system, we need to simultaneously change the charge on object 2 by an amount equal and opposite to ΔQ, so that:

Q1' = Q1 + ΔQ Q2' = Q2 - ΔQ

The new total charge of the system is then:

Qtotal' = Q1' + Q2' = (Q1 + ΔQ) + (Q2 - ΔQ) = Q1 + Q2

We can see that the total charge of the system is conserved, even though the charge on individual objects has changed.

This principle can be expressed mathematically as:

ΔQ1 = -ΔQ2, or ΔQ1 + ΔQ2 = 0

This equation shows that the total charge in a closed system remains constant, even if the charge on individual objects changes. In other words, charge is conserved.

Therefore, we can conclude that while individual charges on objects can be changed, the total charge of a closed system remains constant due to the principle of charge conservation.

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