L17 Ch29 Bio-Savart Law...PHYS.1440 Lecture 17A.Danylov Department of Physics and Applied Physics...
Transcript of L17 Ch29 Bio-Savart Law...PHYS.1440 Lecture 17A.Danylov Department of Physics and Applied Physics...
PHYS.1440Lecture17 A.DanylovDepartmentofPhysicsandAppliedPhysics
Lecture 17
Chapter 29
Bio-Savart Law
Physics II
Bye, bye, Electricity.You won’t be missed.
Course website:https://sites.uml.edu/andriy-danylov/teaching/physics-ii/
PHYS.1440Lecture17 A.DanylovDepartmentofPhysicsandAppliedPhysics
The Vector (Cross) Product
=(ab sinθ,directiongivenbytheright‐handrule)
Fromnowon,almostallequationswillhaveacrossproduct
Thecrossproductofvectorsa andb isavectorperpendiculartobotha andb.
[I]Pointfingersinthedirectionofthe1st (a)vector,thenbendtheminthedirectionofthe2nd one(b).Theoutstretchedthumbwillgiveadirectionofthecrossproduct
[II]Usethreefingersasshowninthefigure
Orderisimportantinthecrossproduct:
PHYS.1440Lecture17 A.DanylovDepartmentofPhysicsandAppliedPhysics
(I) Bio-Savart Law
The electric field produced by a point charge
By analogy, we should have something similar for a magnetic field, B.
?
Magnetic field expression was found experimentally.So, there is no derivation
describes magnetic field of a moving charge
PHYS.1440Lecture17 A.DanylovDepartmentofPhysicsandAppliedPhysics
Bio-Savart LawThe magnetic field of a charged particle q moving with velocity v is given by (I) the Biot-Savart law (for a point charge):
Note that the component of B parallel to the line of motion is zero.
(II) Biot-Savart law (for a current)Consider a current I. Take a small segment ds.Its contribution to a magnetic field at a point of observation is:
q Iv ds
PHYS.1440Lecture17 A.DanylovDepartmentofPhysicsandAppliedPhysics
The Units of B
The SI unit of magnetic field strength is the tesla, abbreviated as T:
1 tesla = 1 T = 1 N/A m
The constant 0 in the Biot-Savart law is called the permeability constant:
0 = 4× 10-7 T m/A = 1.257 × 10-6 T m/A
200‐ton superconducting magnet (Argonne National Laboratory)
ConcepTest B field of qA)IntothescreenB)OutofthescreenC)UpD)DownE)Left
Whatisthedirectionofthemagneticfieldatthepositionofthedot?
PHYS.1440Lecture17 A.DanylovDepartmentofPhysicsandAppliedPhysics
Magnetic field of an infinitely long straight wire with current
If we integrate the BS law equation
2d a perpendicular distance from the wire.
(RHR#2)
(This integration is not trivial, so we skip it and derive the formula later using Ampere’s Law)B‐?
How can we find a B direction?
for an infinitely long straight wire with current, we will get: