AP Physics 2- 10.2 Conservation of Electric Charge and the Process of Charging- Study Notes- New Syllabus
AP Physics 2- 10.2 Conservation of Electric Charge and the Process of Charging – Study Notes
AP Physics 2- 10.2 Conservation of Electric Charge and the Process of Charging – Study Notes – per latest Syllabus.
Key Concepts:
- Conservation of Electric Charge
- Process of Charging
Conservation of Electric Charge
The law of conservation of electric charge states that the net electric charge of an isolated system remains constant over time, regardless of the processes happening within the system.
Key Points:
- Charge can be transferred from one body to another but cannot be created or destroyed.
- Total charge before and after an interaction remains the same.
- In particle interactions, such as nuclear decay or collisions, charge is always conserved.
- Mathematically:
\( Q_{initial} = Q_{final} \)
- Applies universally — from atomic scale (electron-proton interactions) to cosmic scale (stars, plasmas).
Implications:
- Explains why charge is quantized in integer multiples of the elementary charge (\( e = 1.6 \times 10^{-19} \, C \)).
- In electrostatic induction, total charge is conserved while redistribution occurs.
In circuit analysis, conservation of charge leads to Kirchhoff’s Current Law (KCL):
Sum of currents entering a junction = Sum of currents leaving the junction.
Example :
Two conducting spheres, one with charge \( +6 \, \mu C \) and another with charge \( -2 \, \mu C \), are brought into contact and then separated. Find the final charge on each sphere if they are identical.
▶️ Answer/Explanation
Total charge initially: \( Q_{total} = (+6 \, \mu C) + (-2 \, \mu C) = +4 \, \mu C \)
Since the spheres are identical, charge is shared equally:
\( Q_{final} = \dfrac{Q_{total}}{2} = \dfrac{4}{2} = +2 \, \mu C \)
Answer: After contact, each sphere has \( +2 \, \mu C \).
Process of Charging
Charging is the process by which an object acquires an electric charge (positive or negative). This can be done by transferring electrons between objects, while the total charge is conserved.
Methods of Charging:
Charging by Friction:
- When two insulating materials are rubbed together, electrons are transferred from one to the other.
- The material that loses electrons becomes positively charged; the one that gains electrons becomes negatively charged.
- Example: Rubbing a balloon on hair.
Charging by Conduction (Contact):
- A charged object touches another neutral conductor → electrons are transferred until charges are shared.
- Both objects end up with the same sign of charge.
- Example: A charged metal rod touching an uncharged metal sphere.
Charging by Induction:
- A charged object is brought near (without touching) a neutral conductor → charges within the conductor redistribute.
- Grounding the conductor allows transfer of charge, leaving it with a net charge opposite to the inducing object.
- Example: Bringing a negatively charged rod near a metal sphere connected to the ground leaves the sphere positively charged.
Key Points:
- Only electrons move during charging; protons remain bound in nuclei.
- Total charge is conserved during any charging process.
- Conductors allow easy charge movement, while insulators hold charges in place.
Example :
A negatively charged rod is brought near (but does not touch) a neutral metal sphere that is grounded. Describe the charge on the sphere after removing the ground and then the rod.
▶️ Answer/Explanation
Step 1: The negative rod repels electrons inside the sphere, pushing them into the ground. The sphere becomes positively charged (due to loss of electrons).
Step 2: The ground is disconnected while the rod is still present → the sphere remains positively charged.
Step 3: When the rod is removed, the sphere retains the net positive charge.
Answer: The sphere ends up with a net positive charge.