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Application of Coulomb’s Law

Coulomb’s law helps determine the force between two charged particles, such as in atomic physics and electrostatic equilibrium problems.

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AP Physics C Electricity and Magnetism: Gauss’s Law and Electric Fields

Gauss’s Law is a powerful tool for calculating electric fields when there is symmetry.

Gauss’s Law Formula

$$\oint \mathbf{E} \cdot d\mathbf{A} = \frac{Q_{\text{enc}}}{\varepsilon_0}$$Where:

• 
  
• 
  $dA$ 

  = Differential area element

• 
  $Q_{\text{enc}}$ 

  = Charge enclosed

• 
  $\varepsilon_0$ 

  = Permittivity of free space

Common Applications

• Spherical Symmetry: Electric field outside a charged sphere
• Cylindrical Symmetry: Electric field due to an infinite charged wire
• Planar Symmetry: Field near an infinite charged plane

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Electric Potential and Capacitance

Electric potential is the work done per unit charge in moving a charge in an electric field.

Capacitor Applications

Capacitors are widely used in:

• Circuit design
• Energy storage (batteries, power backups)
• Filtering signals in electronics

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This section covers Ohm’s Law, circuit equations, and power relationships.

Ohm’s Law

$$V=IR$$

 

$$V = IR$$

 

Where:

• 
  $V$ 

  = Voltage

• 
  $I$ 

  = Current

• 
  $R$ 

  = Resistance

 

Application in Circuits

• Series Circuits: Total resistance is the sum of individual resistances.
• Parallel Circuits: Inverse of total resistance is the sum of individual reciprocals.

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Magnetism and Magnetic Fields

Magnetism arises from moving charges and currents. The key equations include:

 

Applications of Magnetism

• Electric motors
• Magnetic resonance imaging (MRI)
• Electromagnetic levitation

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Induction and Electromagnetic Waves

Faraday’s Law and Lenz’s Law describe how changing magnetic fields induce voltage.

Faraday’s Law

 

$$\mathcal{E} = -N \frac{d\Phi}{dt}$$ 

Where:

• 
  $\mathcal{E}$ 

  = Induced EMF

• 
  $N$ 

  = Number of turns

• 
  $\Phi$ 

  = Magnetic flux

Applications of Electromagnetic Induction

• Transformers: Step-up and step-down voltage
• Generators: Convert mechanical energy into electricity
• Wireless charging: Uses induction principles

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Final Tips for AP Physics C Exam

1. Understand concepts before memorizing formulas – Many formulas are derived from fundamental laws.
2. Practice problems regularly – Apply formulas to real-world problems.
3. Use diagrams and tables – Visualizing problems makes them easier to solve.
4. Take advantage of online resources – Visit College Board AP Physics C for official information.

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