13.1 Basic Concepts and Formulae
581
B due to a Hollow Cylindrical Shell of Radii a and b (a < b)
B =
μ 0 i(r 2 − a 2 )
2πr (b 2 − a 2 )
(a < r < b)
= 0
(r < a)
=
μ 0 i
2πr
(r > b)
(13.11)
where r is measured from the axis.
B due to a Loop of N Turns and Radius r on the Axis
B =
μ 0 i N R 2
2(R 2 + z 2 ) 3/2
(13.12)
Magnetic Force on a Current-Carrying Wire
The force on the current-carrying wire is directed perpendicular to both the length
of the wire and the field direction. The direction of motion of the wire is given by the
left-hand rule. If the current-carrying wire makes an angle θ with the field direction,
then the force on the wire would be
F = ilB sin θ
(13.13)
Force on Two Parallel Wires Each of Length l Carrying Current i 1 and i 2
and Separated by Distance d
F =
μ 0 li 1 i 2
2π d
(13.14)
The two forces (F 1 due to wire 1 on 2 and F 2 due to wire 2 on 1) form an action–
reaction pair. For parallel currents the wires attract each other and for antiparallel
currents the wires repel each other.
Magnetic Dipole Moment, Magnetic Energy
Magnetic Material, Hall Effect
The magnetic moment produced by a circular current i enclosing an area A is given
by
μ = Ai
(13.15)