Forces acting on a Small Body in the Magnetic Field.-If a small magnet of length ds and pole-strength m is brought into a magnetic field such that the values of the magnetic potential at the negative and positive poles respectively are V 1 and the work done upon the magnet, and therefore its potential energy, will be W =m(V2-Vi) =mdV, which may be written W =m d s- = M d v= - MHo = - vIHo, ds ds where M is the moment of the magnet, v the volume, I the magnetization, and Ho the magnetic force along ds.
Then, if Q be any radiant point and Q' its image (primary focus) in the spherical mirror AP, we have 1 1 2cos4) v l + u 'a ' ' where v 1 = AQ', u =AQ, a =OA, =angle of incidence QAO, equal to the angle of reflection Q'AO.
11,1r; and we get in terms of v 1 1.3.5 18.104.22.168.9 C ' ?
When the cylinder r =a is moved with velocity U and r =b with velocity U 1 along Ox, = U b e - a,1 r +0 cos 0 - U ib2 - 2 a, (r +Q 2 ') cos 0, = - U be a2 a2 (b 2 - r) sin 0 - Uib2 b1)a, (r - ¢2 sin 0; b and similarly, with velocity components V and V 1 along Oy a 2 b2 ?= Vb,_a,(r+r) sin g -Vi b, b2 a, (r+ 2) sin 0, (17) = V b, a2 a, (b2 r) cos 0+Vi b, b, a, (r- ¢ 2) cos h; (18) and then for the resultant motion z 2zz w= (U 2 + V2)b2a a2U+Vi +b a b a2 U z Vi -(U12+V12) b2 z a2b2 Ui +VIi b 2 - a 2 U1 +Vii b 2 - a 2 z The resultant impulse of the liquid on the cylinder is given by the component, over r=a (§ 36), X =f p4 cos 0.ad0 =7rpa 2 (U b z 2 + a 2 Uib.2bz a2); (20) and over r =b Xi= fp?
Hence V 2 - V 1 = - A log R 2 /R 1.
Let V 1 and V2 be the potentials of the plates, and let a charge Q be given to one of them.
Then when the inner cylinder is at potential V 1 and the outer one kept at of two potential V 2 the lines of electric force between the cylinders Q (4).
The position of the central ordinate is given by x = v 1 /po, and therefore is given approximately by pl/po.
() VC1 v.4 t i ITN1-1"t'eC .1C* A t i[rt C :YC)Y(:1 V 5 1 t t 7.C)Y 1'71t?C,'1'J.?.A.
Sumpner in 1891, an electrostatic voltmeter is employed to measure the fall of potential V 1 down any inductive circuit in which it is desired to measure the power absorption, and also the volt-drop V2 down an inductionless resistance R in series with it, and also the volt-drop V3 down the two together.
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B p C v 1 A" FIG.
This will become zero if V 1 is 2V 2, that is, if the linear velocity of the cupcentres is one-half that of the jet of water impinging upon them.
Assuming the electrometer to obey the above-mentioned theoretical law, the first reading is proportional to v 1 -v 2) and the second to v, - v 2 The difference of the readings is then proportional to (0, - v2) (v, - v3).
Heb 3 v 1 " Therefore, holy brethren, partakers of the heavenly calling " .
The value of v 1 can be obtained from Newtonian mechanics to adequate accuracy.
vertex v 1.
For two thin lenses separated by a distance D the condition for achromatism is D = (viii+v2f2) (vi+v2); if v 1 =v (e.g.
Dijkstra 's algorithm is as follows: Input: A graph G and a specified vertex v 1.
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