Last Minute Lecture

Groundwater Explained — Aquifers, Water Table, Contamination & Karst Landscapes | Chapter 19 from Earth: Portrait of a Planet What lies beneath our feet, silently shaping landscapes and supplying our daily water? Chapter 19 of Earth: Portrait of a Planet by Stephen Marshak dives into the world of groundwater—the hidden reserve that sustains ecosystems, agriculture, and cities. For a podcast summary, watch the chapter video on YouTube , or read on for a complete breakdown. What is Groundwater and Where Does it Reside? Groundwater is the largest reservoir of liquid freshwater on Earth, filling the pore spaces and fractures in rock and sediment below the surface. It accumulates through infiltration —rain and snowmelt percolating downward until it reaches the water table , the boundary between unsaturated and saturated zones. Porosity, Permeability, Aquifers, and Aquitards Porosity: The percentage of a rock’s volume that is open space—higher porosity means more storag...

Sources of Magnetic Fields Explained | Chapter 28 of University Physics Chapter 28 explores how moving charges and currents create magnetic fields, and how materials respond to those fields. You’ll master the Biot–Savart Law for calculating field contributions, Ampère’s Law for symmetric configurations, and the role of magnetic susceptibility and permeability in different materials. Watch the full video summary for detailed derivations and visualizations. Magnetic Field from a Moving Charge A single charge moving with velocity v generates a magnetic field given by the equation: B = (μ₀/4π) · [q v × r̂ / r²] Here, μ₀ is the magnetic constant, q the charge, and r̂ the unit vector from the charge to the field point. The field lines form closed loops and obey the superposition principle. Biot–Savart Law & Applications The Biot–Savart Law extends this idea to current elements: dB = (μ₀/4π) · [I dl × r̂ / r²] By integrating over a wire, you find: Long straight wir...