PHYSICS S5 Unit 7: Electric Field Potential and Gravitational Potential

What Will You Learn?

• The course Unit 7: Electric Field Potential and Gravitational Potential will teach you a powerful, scalar approach to analyzing fields. Instead of dealing with the vector quantities of force (F) and field (E or g), you will use the concept of potential (V or VG) and potential energy (U) to solve problems related to electric charges and masses.
• This unit focuses on recognizing the strong analogy between the electric and gravitational fields because both are conservative, inverse-square law forces.
• I. Electric Potential and Energy
• You will learn to analyze the energy stored in a system of charges:
• • Electric Potential Energy (UE): You will define and calculate the work done to assemble a system of charges. For two point charges (Q and q) separated by distance r:
• UE = k Qq/r
• • Electric Potential (V): You will define Electric Potential as the potential energy per unit charge, a scalar property of the field itself. It is measured in Volts (V).
• V = UE/q
• • Potential Difference (Voltage): You will use the potential difference (ΔV) to calculate the work done (W) to move a charge (q) between two points:
• W = q /ΔV
• • Field-Potential Relationship: You will understand the crucial relationship that the Electric Field (E) points in the direction of decreasing potential and is equal to the negative gradient of the potential (E = -dV/dx).
• • Equipotential Surfaces: You will learn about equipotential surfaces—surfaces where the potential is constant—and their property of being always perpendicular to the electric field lines.
• II. Gravitational Potential and Energy
• You will apply the same potential concepts to the force of gravity, particularly for objects far from Earth's surface.
• • Gravitational Potential Energy (UG): You will learn the general formula for potential energy between two masses (M and m) separated by r. Note that UG is always negative because gravity is attractive, and UG is zero at infinity:
• UG = -G Mm/r
• • Gravitational Potential (VG): You will define Gravitational Potential as the potential energy per unit mass, a scalar property of the mass distribution. It is measured in Joules per kilogram (J/kg):
• VG = UG/m = -G M/r
• • Escape Velocity: You will apply the Conservation of Energy principle to calculate the escape velocity—the minimum speed required for an object to completely break free from a planet's gravitational pull.
• III. Synthesis and Problem Solving
• The goal of the unit is to replace the complexity of vector addition (used for forces and fields) with the simplicity of scalar addition (used for potentials and energies) to solve field-based problems efficiently.