AP Physics C E&M- 8.2 Conservation of Electric Charges and Process of Charging- Study Notes- New Syllabus
AP Physics C E&M- 8.2 Conservation of Electric Charges and Process of Charging – Study Notes
AP Physics C E&M- 8.2 Conservation of Electric Charges and Process of Charging – Study Notes – per latest Syllabus.
Key Concepts:
- Conservation of Charge
- Process of Charging
Conservation of Charge
The principle of conservation of charge states that the total electric charge in an isolated system remains constant. Charge can be transferred from one object to another, but it cannot be created or destroyed.
Key Features:
- The algebraic sum of charges before and after any physical or chemical process is the same.
- Charge may redistribute among objects in contact or by induction, but the total amount is unchanged.
- Measured in all known interactions: nuclear reactions, particle collisions, and everyday processes.
Mathematical Expression:
\(\mathrm{Q_{initial} = Q_{final}}\)
Examples of Behavior:
- If a positively charged object touches a neutral one, some charge is transferred, but the combined charge equals the original total.
- In particle reactions, such as beta decay, the sum of charges of all products equals the sum of charges of reactants.
Example :
A neutral metal sphere is touched by a rod with charge \(+6 \, \mu C\). The rod transfers \(+2 \, \mu C\) of charge to the sphere. What are the final charges of the rod and the sphere?
▶️ Answer/Explanation
Step 1: Initial total charge: \(Q_{total} = +6 \, \mu C + 0 = +6 \, \mu C\)
Step 2: After transfer: Sphere: \(+2 \, \mu C\), Rod: \(+6 – 2 = +4 \, \mu C\)
Step 3: Final total charge: \(Q_{final} = +4 \, \mu C + +2 \, \mu C = +6 \, \mu C\)
Final Answer: Sphere = \(+2 \, \mu C\), Rod = \(+4 \, \mu C\), total charge conserved.
Process of Charging
Charging is the process by which an object acquires an electric charge, either by gaining or losing electrons. Since protons are fixed in the nucleus, only electrons are transferred during charging. The total charge of the system is always conserved.
1. Charging by Friction
When two insulating objects are rubbed together, electrons are transferred from one material to the other.
- The object that loses electrons becomes positively charged, and the object that gains electrons becomes negatively charged.
- This process explains everyday phenomena such as static electricity when rubbing a balloon against hair or wool.
\(\mathrm{Q_{initial} = Q_{final}}\) (total charge of the two-body system remains constant)
Example: Rubbing a rubber rod with fur transfers electrons from the fur to the rod. The rod becomes negatively charged, while the fur becomes positively charged.
2. Charging by Conduction
Occurs when a charged object touches a neutral conductor.
- Electrons move between the two objects until they reach the same electric potential.
- The neutral conductor acquires a net charge of the same sign as the charged object.
- This process requires direct physical contact.
\(\mathrm{Q_{final,1} + Q_{final,2} = Q_{initial,total}}\)
Example: A positively charged rod touches a neutral metal sphere. Electrons flow from the sphere to the rod. After separation, the sphere is left with a net positive charge.
3. Charging by Induction
A charged object is brought near a neutral conductor, without touching it.
- The electric field of the charged object causes charges inside the neutral conductor to rearrange:
- Electrons are attracted toward the external positive charge or repelled away from a negative charge.
- If the conductor is temporarily grounded, electrons will either leave or enter from the Earth.
- When the ground is removed and then the external charged object is taken away, the conductor is left with a net charge opposite to that of the external object.
- This process does not require contact; it uses the influence of the nearby electric field.
Example: A negatively charged rod is brought near a neutral metal sphere. Electrons in the sphere are repelled to the far side. If the sphere is grounded, electrons escape into the ground. When the ground is removed, the sphere is left positively charged even though the rod never touched it.
Conservation of Charge:
In all charging processes, the total electric charge of the system remains unchanged:
\(\mathrm{Q_{initial,total} = Q_{final,total}}\)
Example:
A rubber rod is rubbed with fur. If the rod acquires a charge of \(-6 \, \mu C\), what is the charge on the fur?
▶️ Answer/Explanation
Step 1: By conservation of charge, the total charge of the system remains constant.
Step 2: If the rod gains \(-6 \, \mu C\) of charge, the fur must lose the same amount of charge.
Step 3: Charge on the fur = \(+6 \, \mu C\).
Final Answer: Fur has \(+6 \, \mu C\) of charge.
Example :
A metal sphere initially neutral is touched by a rod with a charge of \(+8 \, \mu C\). After contact, \(+3 \, \mu C\) of charge is transferred to the sphere. What are the final charges of the rod and the sphere?
▶️ Answer/Explanation
Step 1: Initial total charge of the system = \(+8 \, \mu C\).
Step 2: Sphere gains \(+3 \, \mu C\). By conservation, the rod must lose the same charge.
Step 3: Final charges: Sphere = \(+3 \, \mu C\), Rod = \(+8 – 3 = +5 \, \mu C\).
Final Answer: Rod = \(+5 \, \mu C\), Sphere = \(+3 \, \mu C\).
Example:
A negatively charged rod is brought near a neutral metal sphere. The sphere is grounded while the rod remains nearby. After the ground is removed and then the rod is taken away, what is the net charge on the sphere?
▶️ Answer/Explanation
Step 1: The negative rod repels electrons in the sphere to the far side.
Step 2: Grounding allows these excess electrons to leave the sphere.
Step 3: When the ground is removed, the sphere has a deficit of electrons, leaving it positively charged.
Step 4: Finally, when the rod is removed, the sphere retains the positive charge.
Final Answer: The sphere becomes positively charged.