Electric Potential. Outline. Potential Energy per Unit Charge. Potential Difference. Potential Energy Difference. Quiz Thursday on Chapters 23, 24.

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Julius Richards
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1 lectic otential Quiz Thusay on Chaptes 3, 4. Outline otential as enegy pe unit chage. Thi fom of Coulomb s Law. elations between fiel an potential. otential negy pe Unit Chage Just as the fiel is efine as foce pe unit chage, the potential is efine as potential enegy pe F unit chage: an U The SI unit fo potential is the volt. (11J/C) otential is often casually calle voltage. s with potential enegy, it is eally the potential iffeence which is impotant. otential negy Diffeence If a chage is oiginally at point, an we then move it to point, the potential enegy will incease by the amount of wok we have one in caying the chage fom to. U s U W F et W F et s s otential Diffeence The potential iffeence between point an point is this wok pe unit chage. W F et s s s

2 elation between an otential elative to Infinity We have efine potential iffeence. ut to have a value fo itself we nee to ecie on a zeo point. In cicuits, we efine the eath to have 0, an often goun the cicuit. n etc. In electostatics we nomally efine 0 fa away fom all chages. Then at point we wite () to mean () - (). otential at a point The potential at point is the wok euie to bing a one-coulomb test chage fom fa away to the point. ( ) s F s s ample 1: Unifom Fiel (0) ( ) Wok foce X istance Wok euie to push a 1-coulomb test chage against the fiel fom to 0. Q.4-1 Suppose, using an yz cooinate system, in some egion of space, we fin the electic potential is ( ) whee is a constant. What is the -component of the electic fiel in this egion?.. C. 0% 0% 0%.. C. 30 Q. 4-1 Given ( ) whee is has the constant value 5 / m. What is the -component of the electic fiel? Solution: (1) () (3)

3 Futhemoe What ae the y an z components of the electic fiel in the pevious uestion? y an also y y 0 z 0 Q Case of a Single oint Chage ) ( ) s ( ) s ( ( ) kq kq 1 1 kq kq Coulomb s Law fo otential is not a ecto So we now have a thi fom of Coulomb s Law: 1.. F kq / kq / 3. kq / ing foces an fiels means aing vectos: fining the esultant vecto. ing potentials means aing numbes, an taking account of thei signs. ut it is much simple than aing vectos. Thus the thi fom of Coulomb s Law is the simplest! ample 1: ing otentials a a Q. 4- Unifomly chage o with chage of Q bent into ac of 10 with aius. What is (), the electic potential at the cente? Q a -Q kq kq ( ) + + a a 1 Note that the fiel at point is not zeo! 0 kq kq kq kq ( 1) + () (3) (4)

4 Q.4-. +kq/. -kq/ C. +kq/ D. -kq/ Unifomly chage o with chage of Q bent into ac of 10 with aius. What is (), the electic potential at the cente? 0% 0% 0% 0%.. C. D. 10 Q. 4- What is (), the electic potential at the cente? Solution: ll bits of chage ae at the same istance fom. Thus k k ( Q) kq kq kq kq ( 1) + () (3) (4) k otential negy of Some Chages The potential enegy U of a goup of chages is the wok W euie to assemble the goup, binging each chage in fom infinity. We can show that the esult is U U1 + U13 + U3 + Whee the potential enegy of each pai is of the fom U k 1 1 / 1 ining negy If the total potential enegy U of a goup of chages is negative that means we have to o wok to pull them apat. The magnitue of this negative potential enegy is calle the bining enegy. amples: emoving an electon fom an atom to fom a positive ion. emoving a space pobe fom eath s gavitational fiel. ample 3: Chage ing In Ch. the fiel of a chage ing is calculate. Hee we compute fist an then use it to get. Get at on ais of cicula ing, a istance z fom cente: ( ) kq ( ) ample 3 Continue Key point: ll bits of chage ae the same istance fom point! kq k Q kq + z Note we have no stuggling with angles o aing many little vectos as we o if we compute.

5 Using to get Now that we have on the ais we can get on the ais by iffeentiation: z This is slightly messy, but we just nee to n emembe that f n 1 f nf z z whee hee 1/ f n ( + z ) ( z) So finally we get kq z + z kqz ) 3/ ( + z which is eactly the esult the tetbook gets in Ch. by iect integation of the fiel. n also: y z y y 0 z 0 Futhemoe What ae the y an z components of the electic fiel in the pevious uestion? y an also y y 0 z 0 Summay of asics U kq/ W ( ) etc. Channel Setting Instuctions fo esponseca F 1. ess an elease the "GO" button.. While the light is flashing e an geen, ente the igit channel coe (ie. channel 1 01, channel 1 1). 3. fte the secon igit is entee, ess an elease the "GO" button. 4. ess an elease the "1/" button. The light shoul flash yellow to confim.

SPH4UI 28/02/2011. Total energy = K + U is constant! Electric Potential Mr. Burns. GMm

SPH4UI 28/02/2011. Total energy = K + U is constant! Electric Potential Mr. Burns. GMm 8//11 Electicity has Enegy SPH4I Electic Potential M. Buns To sepaate negative an positive chages fom each othe, wok must be one against the foce of attaction. Theefoe sepeate chages ae in a higheenegy