Institutt for fysikk, NTNU TFY4155/FY1003: Elektrisitet og magnetisme Spring 2005

Summary, week 15 (April 12 and 13)

Magnetic force on electric current [FGT 28.4; YF 27.6; TM 26.1; AF 24.9; LHL 23.2; DJG 5.1.3]

Straight conductor, length L, current I:

F = IL × B

In general: Conducting wire with length L, current I, arbitrary shape on conductor:

F = ∫_{L} dF = I ∫_{L} dl × B

Magnetic force between parallel current-carrying wires [FGT 29.1; YF 28.4; TM 27.2; AF 24.14; LHL 23.5]

Force pr unit length between parallel wires with current I_{1} and I_{2}, respectively:

f = \frac{μ_{0}I_{1}I_{2}}{2πr}

where r is the distance between the wires. Same direction for the currents ⇒ attraction Opposite direction for the currents ⇒ repulsion

Ampere’s law [FGT 29.1, 29.3; YF 28.6, 28.7; TM 27.4; AF 26.2; LHL 23.6; DJG 5.3]

∮ B · dl = μ_{0}I_{in}

for closed integration curve enclosing stationary current I_{in}. Is valid for arbitrary closed curve and arbitrary current I. Sign on the current according to the right hand rule.

Ampere’s law is useful when we have a suitable symmetry in the problem, so that the integral on the left hand side becomes easily solvable.

Magnetic field from infinitely long solenoid that is tightly wound: Inside the solenoid:

B = μ_{0}nI

with I = current in wire and n = number of turns pr unit length. I.e., uniform magnetic field inside long solenoid. Outside the solenoid, B = 0.

Next week: Gauss’ law for the magnetic field. Summary, electrostatics and magnetostatics: Maxwell’s equations. Different types of magnetism: Paramagnetism, diamagnetism, ferromagnetism.