1. Electricity & Magnetism
Seb Oliver
Lecture 14:
Biot-Savart Law

2. Summary: Lecture 13 Practical uses of moving charge in magnetic field
Lorentz Force
Force on Wire

3. Biot-Savart Law

4. Introduction
We have discussed how an existing magnetic field influences moving charges (and thus currents)
We have not yet discussed the origin of magnetic fields
We will now see that currents (moving charges) produce magnetic fields
This can be thought of as the basic mechanism by which all magnetic fields are produced

5. History
1819 Hans Christian Oersted discovered that a compass needle was deflected by a current carrying wire
Then in 1920s Jean-Baptiste Biot and Felix Savart performed experiements to determine the force exerted on a compass by a current carrying wire
There results were as follows …

6. Jean-Baptiste Biot & Felix Savart’s Results
dB the magnetic field produced by a small section of wire
ds a vector the length of the small section of wire in the direction of the current
r the positional vector from the section of wire to where the magnetic field is measured
I the current in the wire
 angle between ds & r dB r  ds

7. Biot & Savart’s Results
dB perpendicular to ds
dB perpendicular to r
|dB| inversely proportional to |r|2
|dB| proportional to current I
|dB| proportional to |ds|
|dB| proportional to sin q

8. Biot – Savart Law All these results could be summarised by one “Law”
Putting in the constant
Where m0 is the permeablity of free space

9. Magnetic Field from Biot-Savart Law
We can use the Biot-Savart law to calculate the magnetic field due to any current carrying wire
dB2
dB1
dBi
dsi r2 ri
B = dB1+dB2+…+dBi
I.e. B =SdB r1
ds2
ds1

10. One Example of using the Biot-Savart Law
Direction of the field around a long wire

11. Magnetic Field from Biot-Savart Law
We can use the Biot-Savart law to see the direction of the field due to a wire segment
dB1
dB1 r1 r1
ds1 ds r dB

12. Another Right-Hand Rule

13. Magnetic Field from Biot-Savart Law
dB1 r1
c.f.
Of course there is no such thing as an isolated current segment!

14. Summary: Lectures 14 & 15 Biot-Savart Law Force between two wires
(Field produced by wires)
Centre of a wire loop radius R
Centre of a tight Wire Coil with N turns
Distance a from long straight wire
Force between two wires
Definition of Ampere