PHYS117B: Lecture 6 Electric field in planar geometry. Electric potential energy.

1. PHYS117B: Lecture 6Electric field in planar geometry. Electric potential energy. • Last lecture: • Properties of conductors and insulators in electrostatic equilibrium • E = 0 inside the conductor and all excess charges are on the surface • Used Gauss’s law to find the field in and out of spheres (conductors and insulators) … and similarly we can do spherical shells and spheres inside spherical shells • The electric field outside a sphere is = to the E of a point charge located in the center • We “played’ with cylinders the previous time J.Velkovska, PHYS117B

2. The electric field of an infinite charged plane • Use symmetry: • The field is ┴ to the surface • Direction: away from positive charge, and toward a negative charge • Use Gauss’s law to determine the magnitude of the field J.Velkovska, PHYS117B

3. Here’s how we do it: … as easy as 1,2,3 • Choose a Gaussian surface: • a cylinder would work: the field is ┴ to the area vector on the sides and ║ to the area vector on the top and the bottom of the cylinder • a cube or a parallelogram with sides ║to the surface would work, too • Evaluate the flux through the surface and the enclosed charge • EA +EA = 2EA • Qencl = σ A • Apply Gauss’s law: • E = σ/ 2ε0 The electric field of an infinite plane of charge does NOT depend on the distance from the plane, but ONLY on the surface charge density J.Velkovska, PHYS117B

4. Now add a second plane with opposite charge: parallel plate capacitor • For the negatively charged plane: • Flux : - 2EA • Charge: -σ A • E = σ/ 2ε0 , pointing towards the plane • Use superposition to find the field between the plates and outside the plates: • E=0 , outside the plates • E = σ/ ε0 • Direction : from + to - J.Velkovska, PHYS117B

5. When a lightening strikes You are safe inside your car Use the properties of conductors and Gauss’s law: expel the field from some region in space J.Velkovska, PHYS117B

6. Electric field shielding has multiple uses • If you want to measure the gravitational force between 2 objects (Cavendish balance), you need to make sure that electric forces don’t distort your measurement • Put the one of the objects in a light weight metal mesh (Faraday cage) to screen any stray electric fields • Use a coaxial cable ( has a central conductor surrounded by a metal braid which is connected to ground) to transmit sensitive electric signals J.Velkovska, PHYS117B

7. OK, we know how to get the Electric field in almost any configuration, but what does this tell us about how objects in nature interact ? • Well, we know the definition: • Electric field = Force/unit charge • So if we know E, we can find the force on a charge that is placed inside the field • We can use F= ma and kinematics to find how this charge will move inside the field ( we did this for homework) • Today: we will use conservation of energy – a very powerful approach ! J.Velkovska, PHYS117B

8. Electric potential energy • The potential energy is a measure of the interactions in the system • Define: the change in potential energy by the WORK done by the forces of interaction as the system moves from one configuration to another • Electric force is a conservative force: the work doesn’t depend on the path taken, but only on the initial and final configuration => Conservation of energy J.Velkovska, PHYS117B

9. Charge q2 moves in the field of q1 How can the path not matter ? Well, the work is not just Force multiplied by displacement, it is the SCALAR Product between the two. J.Velkovska, PHYS117B

10. Electric potential energy in a uniform field: a charge inside a parallel plate capacitor J.Velkovska, PHYS117B

11. The potential energy of two point charges • The force is along the radius • The work ( and the change in the potential energy) depends only on the initial and final configuration • The potential energy depends on the distance between the charges J.Velkovska, PHYS117B

12. If we have a collection of charges: J.Velkovska, PHYS117B

13. Graph the potential energy of two point charges • U depends on 1/r and on the relative sign of the charges • Defined up to a constant. We take U = 0 when the charges are infinitely far apart. Think of it as “no interaction”. J.Velkovska, PHYS117B

14. Conservation of Energy in 2 charge system • Total mechanical energy Emech = const • Emech > 0 , the particles can escape each other • Emech < 0, bound system J.Velkovska, PHYS117B

15. 2 examples ( done on the blackboard) • Distance of closest approach for 2 like charges • Escape velocity for 2 unlike charges J.Velkovska, PHYS117B