Comprehensive Study Notes on Electrostatics, Electrodynamics, and Electric Circuits

Coulomb's Law Overview:
- Formula for calculating the electrostatic force ( $F$ ) between two point charges: $F = k \frac{Q_1 Q_2}{r^2}$
- In the provided examples, the constant ( $k$ ) is referenced as: $k = 4 \times 10^9$
- Example parameters provided in the calculations:
  - Distance ( $r$ ): $0,3\,m$
  - Charge snippet: $4 \times 10^{-6}\,C$ (equivalent to $4\,\mu C$ )
  - Intermediate calculation fragment: $18 \times 10^{...}$
Charge Quantification and Nature:
- Fundamental Charge of an Electron ( $q_e$ ): $q_e = -1,6 \times 10^{-19}\,C$
- Formula for Number of Electrons ( $n$ ): $n = \frac{Q}{q_e}$
- Case Study: Charge of $-1,7\,nC$
  - Question: Does a sphere with a charge of $-1,7\,nC$ have a deficiency or an excess of electrons?
  - Answer: It has an excess of electrons.
  - Reasoning: The negative sign indicates the object has gained electrons rather than losing them.
Interaction of Multiple Charges:
- Hypothetical Scenario: What happens if a third sphere with a negative charge is introduced to a system containing charges $X$ and $Y$ ?
- Impact Analysis: The introduction of a third charge will affect the net (total) force experienced by both Sphere $X$ and Sphere $Y$ due to the principle of superposition, where the total force is the vector sum of the individual electrostatic forces exerted by all other charges in the vicinity.

Faraday's Law of Induction:
- Definition: The magnitude of the induced electromotive force (Emf) is directly proportional to the rate of change of magnetic flux linkage.
- Mathematical Formula: $\varepsilon = -N \frac{\Delta \Phi}{\Delta t}$
- Variables Defined:
  - $\varepsilon$ : Induced Emf.
  - $N$ : Number of turns or windings in the coil.
  - $\Delta \Phi$ : Change in magnetic flux (measured in Webers, $Wb$ ).
  - $\Delta t$ : Time interval during which the change occurs (measured in seconds, $s$ ).
Magnetic Flux Calculations:
- Formula for Magnetic Flux ( $\Phi$ ): $\Phi = B \times A$
- Variables Defined:
  - $B$ : Magnetic field strength.
  - $A$ : Area of the face of the coil. The area must be in square meters ( $m^2$ ).
Induction Coil Example:
- Given Specifications:
  - Shape: Square induction coil.
  - Side length: $0,03\,m$ .
  - Number of windings ( $N$ ): $400$ .
  - Placement: Perpendicular to a uniform magnetic field.
  - Change in magnetic flux ( $\Delta \Phi$ ): $-1,4 \times 10^{-3}\,Wb$ .
  - Time duration ( $\Delta t$ ): $0,8\,s$ .
- Task: Calculate the induced Emf ( $\varepsilon$ ) in the coil using Faraday's Law.

Fundamental Concepts:
- Emf: Electromotive force.
- Power ( $P$ ): The rate at which work is done or energy is transferred. Measured in Watts ( $W$ ).
- Resistance ( $R$ ): The opposition to the flow of electric current. Measured in Ohms ( $\Omega$ ).
Ohm's Law:
- Requirement: State Ohm's Law in words (The potential difference across a conductor is directly proportional to the current in the conductor at constant temperature).
Circuit Analysis and Power Calculations:
- Scenario Data:
  - Total power across a parallel branch: $P = 60\,W$ .
- Required Calculations:
  1. Calculate the effective resistance of the parallel combination of resistors.
  2. Identify or calculate the Potential Difference (P.d) or voltage across the branch given the total power is $60\,W$ .
  3. Determine the Current flowing through Ammeter $A_1$ .
Key Power Formulas:
- $P = V \times I$
- $P = I^2 \times R$
- $P = \frac{V^2}{R}$

Question 1: A sphere has a charge of $-1,7\,nC$ . Does it have a deficiency or excess of electrons?
- Response: It has an excess because those gain electrons (negative charge is the result of gaining negatively charged particles).
Question 2: How does the introduction of a third negative sphere affect the net force experienced by $X$ and $Y$ ?
- Response: It alters the vector sum of forces acting on each, necessitating a recalculation of the magnitude and direction of the net force based on the position and magnitude of the new charge.
Question 3: What is the induced Emf if a coil with $400$ windings sees a flux change of $-1,4 \times 10^{-3}\,Wb$ over $0,8\,s$ ?
- Calculation Logic: Apply $\varepsilon = -N \frac{\Delta \Phi}{\Delta t}$ using the provided constants.