Physics 223

30. Sources of the Magnetic Field

30.1 Biot-Savart Law

30.2 Force between two parallel wires

30.3 Ampere’s Law

30.4 Magnetic Field (B) of a Solenoid

30.5 Gauss’s Law in Magnetism

Biot-Savart Law

B= μ0 I / 4π ∫ (ds x r̂� ) / r̂2

r̂r̂r̂r̂

Electric Currents Produce Magnetism

II

B = μ0 I / 2 a

a

Electric Currents Produce Magnetism

Right Hand Rule: Thumb points to B and curled fingers indicate I

II

B

Electric Currents Produce Magnetism

B = μ0 I a2 / 2( a2 + x2 )3/2

B

x

a

Electric Currents Produce Magnetism

Right-Hand Rule: Thumb points to current ( I) and curled fingers indicate B

I

BB

Electric Currents Produce Magnetism

Old wine … New bottle!

I

X

B of Infinitely-Long Wire

I

BB

B = o I / 2 a

B of Finite-Length Wire

I

BB

B = o I [sin θ1 - sin θ2 ] / 4 a

30.2 Force Between Two Currents

F = o I1 I2 L / 2 a

I1 I2

30.3 Ampere’s Law

∫B. ds = 0 I

I

BB

30.4 B of a Solenoid

Application of Ampere’s Law

∫B. ds = 0 I

B L = 0 N I

B = 0 N I /L

B = 0 n I

L

30.5 Gauss’s Law in Magnetism

∫B. dA = B

Flux Through the Rectangular Loop

B = 0 I b/2 ln(1 + a/c)

I

X X

X X

X X

X X

X X

c

a

b

That’s all folks!