Last Minute Lecture

Electric Potential & Energy in Electric Fields Explained | Chapter 23 of University Physics Chapter 23 introduces electric potential—a scalar, energy-based perspective on electrostatics that often simplifies calculations compared to vector force approaches. You’ll learn about electric potential energy, voltage (potential difference), equipotential surfaces, and how electric fields relate to potential through gradients and line integrals. Watch the full video summary here for detailed derivations and examples. Electric Potential Energy (U) Electric potential energy ( U ) is stored due to charge configurations. The work done by the field equals the negative change in U: U = (1 / 4πε₀) · (q · q₀) / r for two point charges, with U defined as zero at r → ∞. For multiple charges, sum over unique pairs: U_total = Σ (1 / 4πε₀) · (q_i · q_j) / r_ij . Electric Potential (V) Electric potential ( V ) is the potential energy per unit test charge: V = U / q₀ , thus in volts (J/C...

Potential Energy & Conservation Explained | Chapter 7 of University Physics Chapter 7 introduces potential energy as stored energy due to position or configuration and develops the principle of conservation of mechanical energy—an indispensable tool for solving physics problems with elegance and efficiency. Potential Energy Potential energy (U) represents energy stored within a system. Two key forms appear in this chapter: Gravitational Potential Energy For an object of mass m at height y above a reference level: U grav = m g y As the object moves under gravity, its potential energy converts to kinetic energy. The work done by gravity relates to the change in potential: W grav = –ΔU grav When only gravity does work, K + U remains constant. Elastic Potential Energy Springs store energy when displaced by x , following Hooke’s Law ( F = k x ): U el = ½ k x² Work done by or against a spring between positions x₁ and x₂ is: W = ½ k x₂² – ½ k x₁² In pure spr...