LECTURE 19 EQUIPOTENTIAL SURFACES & ELECTRIC FIELD. Instructor: Kazumi Tolich

Transcription

1 LECTURE 19 EQUIPOTENTIAL SURFACES & ELECTRIC FIELD Instructor: Kazumi Tolich

2 Lecture 19 2 Reading chapter Equipotential surfaces

3 3 Clicker question: 1

4 Equipotential surfaces & electric field 4 Any surface, imaginary or physical, with a constant electric potential is called equipotential surface. Electric field points in the direction of decreasing electric potential. Electric field lines are perpendicular to the equipotential lines. Equipotential surfaces with a fixed potential difference between them are more closely spaced where E is greater. E = ΔV Δs ΔV = EΔs ΔV = -E Δs (large E, small spacing) ΔV = -E Δs (small E, large spacing)

5 5 Clicker question: 2

6 Equipotential surfaces for two charges 6 Equipotential surfaces and electric field lines for two point charges:

7 Example: 1 7 An infinite flat sheet of charge has a uniform surface charge density equal to σ = 3.50 µc/m 2. The electric field due to an infinite sheet of charge is given by E = σ/(2ε 0 ). How far apart are the equipotential surfaces whose potentials differ by 100 V?

8 Example: 2 8 Consider a region of space where a uniform electric field E = 7500 N/C points in the negative x direction. a) What is the orientation of the equipotential surfaces? b) If you move in the positive x direction, does the electric potential increase or decrease? c) What is the distance between the +14 V and the +16 V equipotentials?

9 Charge inside a hollow conductor 9 A small conductor with +q is inside the cavity of a larger conductor. E inside the larger conductor is zero. Electrons accumulate on the inner surface of the shell. All the E lines from +q terminate at the inner surface of the larger conductor. Regardless of how much charge there might be at the outer surface, the smaller conductor is at a higher potential than the larger conductor. If the two were connected with a conducting wire, all the charge on the smaller conductor would flow to the outer surface of the large conductor. You can repeat this to charge the outer surface of the larger conductor indefinitely.

10 Demo: 1 10 Van de Graaff generator Demonstration of electric field lines Production of large potentials Van de Graaff generator produces large potentials. Through contact with the plastic roller, the motorized belt acquires excess electrons from the comb via corona discharge. The electrons flows to the top comb repelled by the belt via corona discharge. The electrons accumulate on the outer surface of the sphere.

11 Hair standing on end 11 This woman was standing on a lookout platform in the Sequoia National Park, which was struck by lightning 5 minutes after she left there. Highly charged cloud above drove electrons down through her body, leaving her head and strands of her hair positively charged. The strands are extended along the direction of E, perpendicular to the equipotential surfaces.

12 Dielectric breakdown 12 Dielectric breakdown occurs when a material is ionized in very high electric fields and becomes a conductor. The magnitude of the E field for which dielectric breakdown occurs in a material is called the dielectric strength of that material. The dielectric strength of air is ~ V/m. In air, the existing ions are accelerated in the electric field, collides with air molecules, ionizing them. The dielectric discharge occurs more often during a dry day because moisture in the air can conduct the charge away before breakdown occurs. The maximum potential in a Van de Graaff generator is limited by the dielectric breakdown of air.

13 Demo: 2 13 Jacob s ladder 15,000 volts applied to two long vertical electrodes forms a spark at the bottom. The electric arc ionizes and heats the air. The heated air rises, and so dose the arc.

14 σ, E, and the shape of a conductor 14 The surface charge density and electric field are larger where the radius of curvature is smaller. Consider the semi-spherical ends of the conductor. V = # = $%() * = (* for a sphere $%& ' ( $%& ' ( & ' V = +,*, = + )* ) since the surfaces of a conductor is equipotential. & ' & ' If r. < r 0, σ. > σ 0. If σ. > σ 0, E. > E 0 since E = * & ' just outside a conductor surface. Dielectric break down occurs where the radius of curvature is the smallest. If a conductor has a sharp point, dielectric breakdown can occur at relatively low potential.

15 Lightning 15 The exact mechanism of how lightning initially forms is still unknown. Charges are separated into layers within the cloud, creating a huge potential difference between the lower part of the cloud and the ground. The negative charge on the lower part of the cloud travels to the ground by ionizing the air. Lightning rods provide a conductive pathway to the ground.

16 2010 eruption of Eyjafjallajokull 16 A static charge was created due to the ash. REUTERS/Lucas Jackson

17 Demo: 3 17 Lightning rod Physical simulation of lightning

18 Electrocardiograph 18 There are electric fields inside the human body. The body is not a perfect conductor, so there are also potential differences. An electrocardiograph plots the heart s electrical activity.

19 Electroencephalograph 19 An electroencephalograph measures the electrical activity of the brain: