30 )(

4 r

rsdiBd

Biot-Savart Law

0 SdB

The Field Produced by a Straight Wire

a

iB

2

0

Field of a Current Carrying Loop

R r

x

2322

20

)(2 xR

RiB

(along x)

30

2 x

MBRx

Ampere’s Law

irdB 0

The field produced by an infinite wire

a

iB

2

0

Problem 4

Consider a very long (essentially infinite), tightly wound coil with n turns per unit length. This is called a solenoid. Assume that the lines of B are parallel to the axis of the solenoid and non-zero only inside the coil and very far away. Also assume that B is constant inside. Find B inside the solenoid if there is a current i flowing through it.

Problem 3

An infinitely long wire has 5 amps flowing in it. A rectangular loop of wire, oriented as shown in the plane of the paper, has 4 amps in it. What is the force exerted on the loop by the long wire?

An infinitely long, hollow cylindrical wire has inner radius a and outer radius b. A current i is uniformly distributed over its cross-section. Find the magnetic field everywhere.

Chapter 10 Quiz

Induced EMF and Inductance

1830s Michael FaradayJoseph Henry

Faraday’s Law of Induction

The induced EMF in a closed loop equals the negative of the time rate of change of magnetic flux through the loop

dt

dEMF B

dt

drdE B

cosBdSdSBSdBd B

S

S

There can be EMF produced in a number of ways:

• A time varying magnetic field• An area whose size is varying• A time varying angle between and • Any combination of the above

B

Sd

R

From Faraday’s law: a time varying flux through a circuit will induce an EMF in the circuit. If the circuit consists only of a loop of wire with one resistor, with resistance R, a current

R

EMFi

Which way?

Lenz’s Law: if a current is induced by some change, the direction of the current is such that it opposes the change.

dt

drdE B

The Moving Circuit

A Simple Generator