ELECTRIC FIELDS… Field diagrams, properties of conductors, and the superposition principle

Warmup 2.0 x electrons are added to a metal ball supported by a plastic stand. §What is the charge of the dome once the electrons are added? §What is the strength of the electric field at a distance of 30 cm from the center of the dome. Which way does it point? §A small Styrofoam ball experiences a force of 0.26 N when placed at this location. What is the charge of the ball? §Your friend Jorge claims that since the dome is in physical contact with the table it is electrically grounded and will be unable to hold a charge. Is he correct? Explain. §Describe a way you could use the negatively charged dome to place a POSITIVE charge.

Electric Field Diagrams 1.Field lines begin on positive source charges (or at infinity) 2.Field lines end on negative source charges (or at infinity) 3.Number of field lines is proportional to the magnitude of the source charge 4.Near field approximation 5.Far field approximation 6.“density” of field lines is an indication of field strength

Examples: §What is the source charge shown on the left? +8  C -16  C

More examples:

Properties of conductors in electric fields: §Electric field is zero inside a conductor §Electric field lines are perpendicular to the surface of a conductor §Field strength is strongest near “pointy parts” §Excess charge resides on the surfaces of a conductor § “unbalanced charge” resides on surface of a conductor §Examples shown on chalk board

Multiple source charges (superposition principle) §Example 1. Find the electric field halfway between a 3nC and a -6nC charge that are separated by 20 cm. Then find the electric field 10 cm to the left of the 3nC charge. §Example 2. The coordinates of a 5 nC charge are (4 cm, 0 cm). The coordinates of an 8 nC charge are (0 cm, 3 cm). Find the electric field at the origin. What force would act on a proton at this point? What force would act on a doubly ionized helium nucleus?

Van de Graaff Generator §Metal dome on insulating stand §Belt driven by a motor charges by friction (charge does NOT come from the outlet!) §Charge is deposited on metal dome (charging by conduction) §Charge moves to outside leaving inside neutral §Amount of stored charge is limited by charge “leakage”, or by arcing (sparks!)

Van de Graaff problems §1. The dome of a Van de Graf generator receives a charge of 0.2 mC. Find the strength of the electric field (a) inside the dome, (b) at the surface of the dome, assuming it has a radius of 12 cm, 36 cm from the center of the dome. §2. If the electric field strength in air exceeds 3.0 x 10 6 N/C the air becomes a conductor. Use this fact to determine the maximum amount of charge that can be carried by a metal sphere 12 cm in radius. 120 cm in radius. §3. A Van de Graaff generator is charged so that the electric field at its surface is 30,000 N/C. Find the initial acceleration of a proton released near its surface.

AP CLASSWORK – ELECTRIC FLUX AND GAUSS’S LAW During a thunderstorm the electric field at the earth’s surface points straight upwards, and may be as strong as 100,000 N/C. §If a hula hoop with a diameter of 1.0 m is inclined at 20 o from the horizontal, what is the electric flux through the surface of the hoop? §Find the acceleration of a proton that is placed in this field. A uniformly charged insulating thread has a charge density of =2  C/cm. What is the strength of the electric field 1.0 m from the thread? What force would an electron experience at this point? A hollow spherical shell of radius 5 cm has 20  C of charge evenly distributed on it’s outer surface.  Find the surface charge density (  ) §What is the electric field outside of the sphere? §What is the electric field inside the sphere?