L17 Ch29 Bio-Savart Law...PHYS.1440 Lecture 17A.Danylov Department of Physics and Applied Physics...

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PHYS.1440 Lecture 17 A.Danylov Department of Physics and Applied Physics 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/

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:

ConcepTest Cross Product

Find a direction of a cross product

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:

PHYS.1440Lecture17 A.DanylovDepartmentofPhysicsandAppliedPhysics

Thank you