592
13 Electromagnetism I
A long cylinder conductor of radius R carries a current I along its length.
The current is uniformly distributed throughout the cross-section of the conductor. Calculate the magnetic field at a distance r = R/2 from the axis of
the conductor. Find the distance r > R from the axis of the conductor where
the magnitude of the magnetic field is the same as at r = R/2.
[University of Durham]
13.45 (a) Show that (ignoring edge effects) the self-inductance, L, of a solenoid
with n turns per unit length, length l and cross-sectional area A, is
given by
L = μ 0 n
2 Al
(b) A solenoid with 100 turns, length 10 cm and of radius 1 cm, carries a
current of 5A. Calculate the magnetic energy stored in the solenoid.
(c) The current in the solenoid of part (b) is reduced to zero at a uniform rate
over 5 s. Calculate the emf induced in the coil.
[University of Durham 2005]
13.46 (a) What is the magnetic field at a point 50 mm from a long straight wire
carrying a current of 3 A?
(b) A small current element I dl with dl = 2 ˆ
k and I = 2 A is centred at the
origin. Find the magnetic field d B at the following points:
(i) on the x-axis at x = 3 m,
(ii) on the x-axis at x = −6 m,
(iii) on the z-axis at z = 3 m,
(iv) on the y-axis at y = 3 m.
[University of Aberystwyth, Wales 2005]
13.47 A thin torus, of radius 0.1 m, is wound uniformly with 100 turns of wire. If
a current of 2.0 A flows through the wire, what are the magnitudes of the B
and H fields generated within the torus if it contains (i) a vacuum and (ii)
a material with relative permeability 500? What is the magnetization in the
material (Fig. 13.13)?
Fig. 13.13
13 Electromagnetism I
A long cylinder conductor of radius R carries a current I along its length.
The current is uniformly distributed throughout the cross-section of the conductor. Calculate the magnetic field at a distance r = R/2 from the axis of
the conductor. Find the distance r > R from the axis of the conductor where
the magnitude of the magnetic field is the same as at r = R/2.
[University of Durham]
13.45 (a) Show that (ignoring edge effects) the self-inductance, L, of a solenoid
with n turns per unit length, length l and cross-sectional area A, is
given by
L = μ 0 n
2 Al
(b) A solenoid with 100 turns, length 10 cm and of radius 1 cm, carries a
current of 5A. Calculate the magnetic energy stored in the solenoid.
(c) The current in the solenoid of part (b) is reduced to zero at a uniform rate
over 5 s. Calculate the emf induced in the coil.
[University of Durham 2005]
13.46 (a) What is the magnetic field at a point 50 mm from a long straight wire
carrying a current of 3 A?
(b) A small current element I dl with dl = 2 ˆ
k and I = 2 A is centred at the
origin. Find the magnetic field d B at the following points:
(i) on the x-axis at x = 3 m,
(ii) on the x-axis at x = −6 m,
(iii) on the z-axis at z = 3 m,
(iv) on the y-axis at y = 3 m.
[University of Aberystwyth, Wales 2005]
13.47 A thin torus, of radius 0.1 m, is wound uniformly with 100 turns of wire. If
a current of 2.0 A flows through the wire, what are the magnitudes of the B
and H fields generated within the torus if it contains (i) a vacuum and (ii)
a material with relative permeability 500? What is the magnetization in the
material (Fig. 13.13)?
Fig. 13.13