Look over Chapter 22 sections 1-8 Examples 2, 4, 5, Look over Chapter 16 sections 7-9 examples 6, 7, 8, 9. Things To Know 1/22/2008 PHYS 2212

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1 PHYS 1 Look ove Chapte sections 1-8 xamples, 4, 5, PHYS 111 Look ove Chapte 16 sections 7-9 examples 6, 7, 8, 9 Things To Know 1) What is an lectic field. ) How to calculate the electic field fo a point chage. 3) What the electic field is between two chages. 4) How to find the electic field fo Two o moe point chages. 5) How to find the acceleation of a chaged object in an electic field. 1

2 Action at a Distance Some foces we can see how the foces is being applied. Some foces poduce an action ove a distance of sepaation. To undestand these foces we use the idea of a Field. A Field is any physical quantity which can be specified simultaneously fo all points within a given egion of inteest. Fields Thee ae two types of fields: A Scala Field - this type of field assigns a value to evey point in space. xample: the tempeatue in a oom. A Vecto Field - this type of field assigns a vecto to evey point in space. xample: The gavitational field aound the M eath. g G The lectic Field To define the lectic Field at some point we imagine placing a small test chage q [taken to be (+)] at the point in space that is to examined, and we measue the electic foce F that acts on this chage. The electic field at this point is then defined as: lim q F q The diection of is given by the diection in which the positive test chage would tend to move.

3 Lines of Foces Michael Faaday, who intoduced the idea of electic fields thought of space aound a chaged object as filled with lines of foce o lectic Field Lines. The elation between the field lines and the electic field vectos is this: At any point, the diection of a staight field line o the diection of a tangent to a cuved field line gives the diection of at that point. Whee the field lines ae close togethe, the magnitude of is lage, and whee they ae fa apat, the magnitude of is small. The lectic Field Lines of a Sphee of Unifom Chage lectic field lines extend away fom positive chage and towads negative chage. of a Point Chage To find the foce on a test chage q due to a (+) point chage q we can use Coulomb s law as: F q 1 q 4 πε The diection of F is away fom q. 3

4 of a Point Chage Then to find the electic field we can use: F lim 4 1 q q q πε Whee as we have seen points away fom q. To find the electic field due to a collection of chages we can use the Supeposition Pinciple. is also a Vecto q u u q q k k ˆ 3 xample 1 1)Thee chages ae at the cones of an equilateal tiangle. What is the electic field at the position of the.µc chage? What is the foce on the.µc chage? 4

5 The lectic Filed of a Continuous Chage Distibution Δq ˆ P Δ up The lectic field at Point P due to a piece of the object is given by: Δq Δ k ˆ The total lectic field is given by the sum ove all the pieces of the object: u Δq dq k lim ˆ k ˆ i Δqi i i i Chage Densities If a chage Q is unifomly distibuted thoughout a volume V the Volume Chage Density: Q ρ V If a chage Q is unifomly distibuted ib t d on a suface Q aea A the Suface Chage Density: σ A If a chage Q is distibuted on a line of length l the Linea Chage Density: λ Q l d a xample dx l )A od of length l has a unifom positive chage distibution λ and a total chage Q. Calculate the electic field at a point which is a distance a fom the end of the od. 5

6 A point Chage in an lectic Field If we want to descibe the motion of a chaged paticle we need to know the acceleation of the paticle. And thus the acceleation is given by F q a m F q m If the paticle has a mass m. xample 3 3)An ink dop with a mass m of kg and a negative chage of magnitude q C entes the egion between the plates, initially moving along the x-axis with speed v x 18m/s. The length L of the plates is 1.6 cm. The plates ae chaged and thus poduce an electic field of magnitude N/C. What is the vetical deflection of the dop at the fa edge of the plates? 6