Magnetostatics

Magnets and Magnetic Fields Magnets have two ends – poles – called north and south. Like poles repel; unlike poles attract.

Magnetic fields ( B )can be visualized using magnetic field lines, which are always closed loops. Magnetic fields is tangential to the field lines. The field is strongest where the field lines are most dense F = qv x B The field is strongest where the field lines are most dense SI units N/(C·m/s) = tesla (T)

Force on Electric Charge Moving in a Magnetic Field The force on a moving charge is related to the force on a current: Once again, the direction is given by a right-hand rule. F = qvBsin θ

Force on Electric Charge Moving in a Magnetic Field If a charged particle is moving perpendicular to a uniform magnetic field, its path will be a circle. The magnetic force is supplying the centripetal force qvB = mv 2 /R  R = mv/qB

Electric Currents Produce Magnetic Fields Experiment shows that an electric current produces a magnetic field.

Force on Electric Charge Moving in a Magnetic Field Problem solving: Magnetic fields – things to remember 1. The magnetic force is perpendicular to the magnetic field direction. 2. The right-hand rule is useful for determining directions. 3. Equations in this chapter give magnitudes only. The right-hand rule gives the direction.

Force on Electric Charge Moving in a Magnetic Field

Magnetic on a Current –Carrying Wire The total force on a wire segment will be N charges travel through the segment in time t = l/v F = N (qvB) The current can be written as I = q/t = Nq/(l/v) = Nqv/l F = IlB

The force on the wire depends on the current, the length of the wire, the magnetic field, and its orientation. This equation defines the magnetic field B. F = IlBsin θ

Consider a rectangular loop of wire with dimension l and w, carrying current i as shown in figure (a). The net torque about the central axis of the loop will be A = area of loop

Magnetic Field due to a Long Wire The field is inversely proportional to the distance from the wire: The constant k’ has the value: B = k’ I/R k’ = 2 x 10-7 Tm/A The field lines created on a long wire form concentric circles on the wire. Long wire rule: Place the thumb of your right hand in the direction of the current. Your fingers will wrap in the direction of the field line circulation.

Force between Two Parallel Wires The magnetic field produced at the position of wire 2 due to the current in wire 1 is: The force this field exerts on a length l 2 of wire 2 is: B = k’ I 1 /d F = l 2 (k’ I 1 I 2 /d)

20.6 Force between Two Parallel Wires Parallel currents attract; antiparallel currents repel.

F = qv x B F = qvBsin θ R = mv/qB F = IlBsin θ net  = iAB sin θ B = k’ I/R F = l 2 (k’ I 1 I 2 /d) Key Formulas