2054Lecture7 - Electric Potential & Work Electric...

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Unformatted text preview: Electric Potential & Work Electric Topics of Discussion Topics A Comparison of Gravitational and Electric Comparison Potential Potential Mechanical Work Electric Potential & Work The Electric Potential of the Point Charge & The the Principle of Superposition the Equipotential Surfaces The Relationship between the Electric Field & The the Electric Potential the Gravitational & Electric Potential Gravitational Recall that the work done in a gravitational field Recall work is the difference between the initial (UA) and is and final (UB) gravitational potential energies. The final gravitational work done is given by WAB = mghA – mghB. The work done in an electric field is the The work difference between the initial (UA) and final (UB) difference electric potential energies. The work done is given by WAB = UA – UB. Work Work Recall that the mechanical work done WAB Recall mechanical in moving a body from point A to point B over a distance s is (Fcosθ)s. The The mechanical force F in an electric field E is mechanical given by F=q0E. So, the mechanical work So, mechanical done WAB in an electric field E by moving a test charge q from point A to point B over a distance s is given by WAB=(qoEcosθ) s. Electric Potential Electric The electric potential V is the potential The electric energy U per unit test charge q0, and is and given by given U V= q0 where the units of electric potential are in where Volts (V) or J/C. Volts or J/C The Electric Potential &Work The The work W done in moving a charge q The from point A to point B per unit test charge is given by is W UA UB = − = V A − VB q0 q0 q0 where the unit of work is the Joule (J). where Joule Electric Potential of a Point Charge Electric The electric potential V is work done in The moving a test charge from infinity to some distance r from a point charge q, and is and given by given 1q V= 4π ε 0 r where the unit of electric potential is the where Volt=J/C. Volt=J/C The Superposition Principle The Let ri be the distance from a point charge Let qi to any observation point P. Then for N Then point charges, the sum of all individual electric potentials Vi at the point P due to the point charges is given by the 1 V = ∑ Vi = 4π ε 0 i= 1 N ∑ N i= 1 qi ri Equipotential Surfaces for Conductors Conductors A surface on which the measurement of surface electric potential at any two points is the same is called an equipotential surface. equipotential Electric field lines enter or exit Electric perpendicular to the surface of a conductor. conductor. Electric field lines pass through an Electric equipotential surface so that they are parallel to the normal of this surface. parallel Each component of the electric field E is Each proportional to the rate change of the electric potential ΔV in that direction Δs. For example, For ˆ the electric field E = E x i + E y ˆ in the plane is j related to the rate change in electric potential in the x- and y-directions, and is either given by xy- The Relationship between the Electric Field & the Electric Potential Potential or ∆V ∆V and E y = − Ex = − and ∆x ∆y ∆V ˆ ∆V ˆ E= − i− j ∆x ∆y ...
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