PHYSICS II ELECTRICITY ELECTRIC POTENTIAL ENERGY AND ELECTRIC POTENTIAL EUROPEAN UNIVERSITY OF LEFKE Assist. Prof. Dr. Nemika CELLATOΔLU 1 ELECTRIC POTENTIAL ENERGY ELECTRIC POTENTIAL ENERGY ELECTRIC POTENTIAL ENERGY ELECTRIC POTENTIAL ENERGY ELECTRIC POTENTIAL • An electric potential is the amount of work needed to move a unit of charge from a reference point to a specific point inside the field without producing an acceleration. • Also electric potential is described as, Electric Potential energy per unit charge. ELECTRIC POTENTIAL • If a positive test charge q in an electric field has electric potential energy at some point (relative to some zero potential energy), the electric potential at this point is; π π= π Note that, only differences in electric potential is meaningful!!!! So, the electric potential difference between point «i» and «f» are meaningful. ELECTRIC POTENTIAL • If the electric potential difference between, «i» and «f» is; ππΉ − πΔ° πππ ΰ΅π πππ = ππ − ππ = =− π The SI unit of potential difference is Volt(V). π½ΰ΅ 1π = 1 πΆ ELECTRIC POTENTIAL IN A UNIFORM ELECTRIC FIELD • Consider a uniform electric field directed along the negative y axis as shown below; Note that E=constant EXAMPLE A battery has a specified potential difference ΔV between its terminals and establishes that potential difference between conductors attached to the terminals. A 12-V battery is connected between two parallel plates as shown below figure. The separation between the plates is d = 0.30 cm, and we assume the electric field between the plates to be uniform. Find the magnitude of the electric field between the plates. SOLUTION EXAMPLE The difference in potential between the accelerating plates in the electron gun of a television picture tube is about 25 000 V. If the distance between these plates is 1.50 cm, what is the magnitude of the uniform electric field in this region? SOLUTION ELECTRIC POTENTIAL OF POINT CHARGES • If we check the electric potential of a point charge shown above figure at point P; EXAMPLE SOLUTION EXAMPLE The three charged particles in below Figure are at the vertices of an isosceles triangle. Calculate the electric potential at the midpoint of the base, taking q= 7.00 µC SOLUTION PHYSICS II ELECTRIC POTENTIAL (CONTINOUS CHARGE DISTRIBUTION) EUROPEAN UNIVERSITY OF LEFKE Assist. Prof. Dr. Nemika CELLATOΔLU 19 ELECTRIC POTENTIAL (CONTINOUS CHARGE DISTRIBUTION) • If we write the electric potential of selected infinitely small charge element dq at point P by using the point charge approach, ELECTRIC POTENTIAL (CONTINOUS CHARGE DISTRIBUTION) πππ ππ = π If we integrate this over the geometry of charge distribution; πππ π=β«Χ¬β¬ π EXAMPLE EXAMPLE EXAMPLE SOLUTION Equipotential Lines and Surfaces • An equipotential surface is one on which all points are at the same potential. • The potential difference between any two points on the surface is zero, so no work is required to move a charge from one point on the surface to the other. Equipotential Lines and Surfaces • Electric potential can be represented by drawing equipotential lines or, in three dimensions, equipotential surfaces. • An equipotential surface must be perpendicular to the electric field at any point Equipotential Lines and Surfaces The Electron Volt, a Unit of Energy • The joule is a very large unit for dealing with energies of electrons, atoms, or molecules. For this purpose, the unit electron volt (eV) is used. ELECTRICITY ELECTRIC POTENTIAL and ELECTRIC FIELD • The electric field and the electric potential V are related as shown in ; βπ βπ = = − β« πΈ Χ¬β¬. ππΤ¦ ππ , • For simplicity if we assume that VΔ°=0, We can write that π = − β« πΈ Χ¬β¬. π πΤ¦ (**) ELECTRICITY ELECTRIC POTENTIAL and ELECTRIC FIELD • We now show how to calculate the value of the electric field if the electric potential is known in a certain region. From Equation (**), we can express the potential difference dV between two points a distance dr apart as; • ππ = −πΈ . π πΤ¦ (***) ELECTRICITY ELECTRIC POTENTIAL and ELECTRIC FIELD • If the electric field has only one component Ex, then Therefore, Equation (***) becomes dV = - Ex dx or • ππ = −πΈπ₯ ππ₯ That is, the x component of the electric field is equal to the negative of the derivative of the electric potential with respect to x. Similar statements can be made about the y and z components ELECTRICITY ELECTRIC POTENTIAL and ELECTRIC FIELD In general, the electric potential is a function of all three coordinates. If V(r) is given in terms of the Cartesian coordinates, the electric field components Ex , Ey, and Ez can readily be found from V(x, y, z) as the partial derivatives. ππ½ ππ½ ππ½ π¬ π, π, π = − π+ π+ π ππ ππ ππ EXAMPLE The electric potential at a certain region is ; π½ π, π, π = πππ ππ ππ π½ππππ A)Find π¬ π, π, π B)Find π¬ π, π, π SOLUTION EXAMPLE The electric potential at a certain region is ; π½ π, π, π = πππ πππ π½ππππ a)Find π¬ π, π, π b)Find π¬ π , π, π SOLUTION
