Current carrying wires1820 Hans Christian Oersted

Hans Christian Ørsted

Biot-Savart Law

3

)(

r

rsdiBd

Infinitesimally small element of a current carrying wire produces an infinitesimally small magnetic field

Sd

i

(Also called Ampere’s principle)

30 )(

4 r

rsdiBd

r

0 is called permeability of free space

2770 )/(104)/(104 ampNmeterampwebers

0 SdB

Ampere’s Law

irdB 0

The field produced by an infinite wire

a

iB

2

0

Problem 6

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.

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?

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

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

cosBdSdSBSdBd B

S

S

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