PHYS_Prelecture starting Oct.15

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Biot savart law used to measure magnetic field produced by an arbitrary current.

AMPERES LAW

integral of magnetic field around a closed path to the current passing through the area defined by that path

Ampere's law has a very close relation with Gauss's law and sometimes can be used to help calculate.

Right hand rule for biot savart law is thumb in direction of current and fingers will curl in the direction of B

Ampere's law

line integral of B * dl = U(0)*I

U(0) is m=mu not

As shown in the following diagram, the strength of the magnetic field B is reduced by a factor of two since it scales like 1/R, and the length of the path L increases by a factor of two since the circumference of a circle scales like R(i.e., C = 2πR). These two factors cancel, and the the net effect is that the integral of B ·dL around the closed path does not depend on the radius of the circle at all:

If B is perpendicular to dl for an integral it is equal to 0

When wire is outside closed path the integral of B dot dl will be = 0

When integrating B is a constant can be pulled out in front of integral and dl for a circular path becomes 2pir still equal to U(0)*I

(r

vs

(r>a) B= U(0)*I/2*pi*r

Potential difference also known as EMF

Electrodynamics, electric fields changing with time.

Changing magnetic fields can create electric fields

at equilibrium E = vB

Potential Difference

EMF = V*B*L

****changing is the area enclosed

Current

I = (V*B*L)/R

Power Dissipated

P = (V*B*L)^2/R

Magnetic field at top segment of the loop is smaller than the magnetic field at the bottom segment of the loop.

EMF of loop = v*L(Vbottom- Vtop)

**** changing is the magnetic field

Generator converts mechanical energy into electrical energy

At Equilibrium magnetic force equals electric force

q*E = q*v*B*cos(theta)

E = v*B*cos(theta)

Motional EMF

EMF = w*W*L*B*cost(w*t)

EMF = w*A*B*cos(w*t)

***changing is the orientation of the loop and the magnetic field

External agent must exert force F to the right to maintain constant v. demonstrated in example of green bar CP2

The EMF itself creates a magnetic flux that opposes the change in flux that it produced

Time rate of change of magnetic flux = B*V*L

EMF also = B*V*L

so Time rate of change of magnetic flux = EMF

Whenever flux changes an EMF is induced!!!!!

This is a fundamental of Faradays Law!

Lenz Law goes into significance of negative sign in Faradays Law

EMF is in the direction that opposes the time rate of change of magnetic flux.

Q1:

Remember the Lenz' law states the induced current will oppose the change in flux. In this case the B field is increasing in the direction out of the screen. In which direction would you have to induce a current in the loop in order to oppose this change

A changing magnetic flux will produce an electric field…Faraday

Flux will change with time if the current changes with time.(around a loop)

Q2:

Even though the flux through the loop is zero at this point, the rate of change of flux through the loop,dΦ/dt, is greatest, resulting the greatest emf.

Self inductance is a chang ein magneticflux or

SI unit for inductance is the henry 1 telsa meter^/arez

Oct.15

o.21,motional emf

Oct 23

Oct29