13.2 Problems
595
(b) Calculate the magnitude of the force when
I 1 = 1 A, I 2 = 4 A, d = 0.10 m, n = 10, and l = 0.05 m.
[University of Durham 2004]
13.59 Two parallel rails of negligible resistance are at distance d apart and are
connected by a resistor of resistance R. A conducting rod lies perpendicular
to the two rails and is free to slide on the rails. A constant magnetic field B
is perpendicular to the loop formed by the rails, rod and resistor. An external
agent drags the rod at velocity v along the rails. Find (a) the current flowing in
the resistor, (b) the total power delivered to the resistor and (c) the magnitude
of the applied force that is needed to move the rod with this velocity.
[University of Durham]
13.2.4 Magnetic Energy, Magnetic Dipole Moment
13.60 In prob. (13.37) show that the magnetic moment of the disc will be μ =
ωq R 2
4
.
13.61 The earth has a magnetic dipole moment of 6.4 × 10 21 A/m
2 . Show that this
dipole moment can be produced by passing a current of 5 × 10 7 A in a single
wire going around the magnetic equator.
13.62 Calculate the energy density at the centre of a circular loop of wire 10 cm
radius carrying a current of 100 A.
13.63 Given that the magnetic field at the centre of hydrogen atom is 13.5 Wb/m 2 ,
calculate the magnetic energy density at the centre of hydrogen atom due to
the circulating electron.
13.64 A wire of length l forms a circular coil. If a current i is set up in the coil show
that when the coil has one turn the maximum torque in a given magnetic field
developed will be
1
4π
l 2 i B
13.65 A charge q is uniformly distributed over the volume of a uniform sphere of
mass m and radiusR, which rotates with an angular velocity ω about the axis
passing through its centre. Show that the ratio of the magnetic moment and
the angular momentum will be
μ
L
=
q
2m
.
13.66 An electric dipole, whose dipole moment has magnitude 1.6 × 10 −29 Cm is
placed in a electric field of 1000 V/m. The direction of the dipole moment
makes an angle of 30 ◦ to the direction of electric field. What is the potential
energy of the dipole?
595
(b) Calculate the magnitude of the force when
I 1 = 1 A, I 2 = 4 A, d = 0.10 m, n = 10, and l = 0.05 m.
[University of Durham 2004]
13.59 Two parallel rails of negligible resistance are at distance d apart and are
connected by a resistor of resistance R. A conducting rod lies perpendicular
to the two rails and is free to slide on the rails. A constant magnetic field B
is perpendicular to the loop formed by the rails, rod and resistor. An external
agent drags the rod at velocity v along the rails. Find (a) the current flowing in
the resistor, (b) the total power delivered to the resistor and (c) the magnitude
of the applied force that is needed to move the rod with this velocity.
[University of Durham]
13.2.4 Magnetic Energy, Magnetic Dipole Moment
13.60 In prob. (13.37) show that the magnetic moment of the disc will be μ =
ωq R 2
4
.
13.61 The earth has a magnetic dipole moment of 6.4 × 10 21 A/m
2 . Show that this
dipole moment can be produced by passing a current of 5 × 10 7 A in a single
wire going around the magnetic equator.
13.62 Calculate the energy density at the centre of a circular loop of wire 10 cm
radius carrying a current of 100 A.
13.63 Given that the magnetic field at the centre of hydrogen atom is 13.5 Wb/m 2 ,
calculate the magnetic energy density at the centre of hydrogen atom due to
the circulating electron.
13.64 A wire of length l forms a circular coil. If a current i is set up in the coil show
that when the coil has one turn the maximum torque in a given magnetic field
developed will be
1
4π
l 2 i B
13.65 A charge q is uniformly distributed over the volume of a uniform sphere of
mass m and radiusR, which rotates with an angular velocity ω about the axis
passing through its centre. Show that the ratio of the magnetic moment and
the angular momentum will be
μ
L
=
q
2m
.
13.66 An electric dipole, whose dipole moment has magnitude 1.6 × 10 −29 Cm is
placed in a electric field of 1000 V/m. The direction of the dipole moment
makes an angle of 30 ◦ to the direction of electric field. What is the potential
energy of the dipole?