Magnetic Field Generated by Current in Straight Wire (1)
Magnetic Field Generated by Current in Straight Wire (1). Consider a field point P that is a distance R from the axis of the wire. ⢠dB = µ0. 4Ï. Idx r2 sinÏ = µ0. 4Ï.
Magnetic Field Generated by Current in Straight Wire (1) Consider a field point P that is a distance R from the axis of the wire. µ0 Idx µ0 Idx sin φ = cos θ 4π r2 4π r2 R R r2 dx = = 2 2 = • x = R tan θ ⇒ dθ cos2 θ R /r R • dB =
µ0 I µ0 I r2 dθ cos θ = cos θdθ • dB = 4π r2 R 4π R Z θ2 µ0 I • B= cos θdθ 4π R θ1 µ0 I (sin θ2 − sin θ1 ) = 4π R • Length of wire: L = R(tan θ2 − tan θ1 )
Wire of infinite length: θ1 = −90◦ , θ2 = 90◦ ⇒ B =
µ0 I 2πR
26/3/2008
[tsl216 – 3/16]
Magnetic Field Generated by Current in Straight Wire (2) Consider a current I in a straight wire of infinite length. • The magnetic field lines are concentric circles in planes prependicular to the wire. • The magnitude of the magnetic field at distance R µ0 I . from the center of the wire is B = 2πR • The magnetic field strength is proportional to the current I and inversely proportional to the distance R from the center of the wire. • The magnetic field vector is tangential to the circular field lines and directed according to the right-hand rule.
26/3/2008
[tsl217 – 4/16]
Magnetic Field Generated by Current in Straight Wire (3) ~ in the limit R → 0. Consider the magnetic field B • B=
Field at center of ring (z = 0): Bz = µ0I. 2R. ⢠Magnetic moment: µ = IÏR. 2. ⢠Field at large distance (z â« R) : Bz â. µ0. 2Ï. µ z3. 28/3/2011. [tsl214 â 6/14]
The symmetry dictates that the magnetic field B is directed tangentially with magnitude B depending on R only. ⢠Current inside loop: IC = I. ⢠Ampère's law ...
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q v à r r2. (2) Force F1 exerted by field B on point charge q1: F1 = q1v1 à B. (1+2) There is a time delay between causally related events over distance.
Apr 3, 2018 - passed to gdsl_rbtree_alloc() (p.214). The binary search tree T is not deallocated itself and its name is not modified. Note. Complexity: O( |T| ).
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