Conservation of Charge
Total electric charge in an isolated system is conserved.
Formula
Variables
Example
Charge is never lost
How it works
In an isolated system, the algebraic sum of all electric charges stays the same, even though charge can move from one object to another. This happens because charge is not created or destroyed in ordinary interactions; it is merely transferred, such as when electrons move during friction, contact, or a circuit process. If a system seems to gain or lose charge, that usually means charge has entered or left the system boundary rather than being produced or destroyed inside it.
When to use it
Use this when analyzing charging by contact, friction, or induction, and whenever you need to track how charge is distributed among objects in a closed system. It is also essential in circuit problems and particle interactions where you must check that total charge before and after remains the same.
Worked example, step by step
A neutral metal sphere is touched by a charged rod, and after separation the rod has a charge of +6 μC. If the rod originally had +10 μC, what was the sphere’s initial charge? Step 1: Write conservation of charge for the isolated rod-sphere system: initial total charge = final total charge Step 2: Let the sphere’s initial charge be q. 10 μC + q = 6 μC Step 3: Solve for q: q = 6 μC - 10 μC = -4 μC Step 4: Check: Initial total = 10 μC + (-4 μC) = 6 μC Final total = 6 μC Answer: The sphere’s initial charge was -4 μC.
Common mistakes to avoid
- Treating charge as if it can disappear instead of only moving between objects
- Forgetting to include all objects in the system when adding charges
- Confusing conservation of charge with conservation of electric potential or electric current
Did You Know?
Electric charge can neither be created nor destroyed, a law that holds even inside exploding stars.
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