13.2 Problems
583
Lenz law: The reason for the minus sign in (13.21) is given by Lenz law which
states ‘the induced current will appear in such a direction that it opposes the change
that produced it’.
If the coil forms a closed circuit then only the induced current can be present,
otherwise in the case of an open circuit one can only speak of induced emf and its
direction.
In a coil of N turns
ξ = −N
ϕ
t
(13.22)
If the circuit is complete current will appear and will be given by
i =
ξ
R
= −
N
R
ϕ
t
(13.23)
where R is the resistance of the circuit. The corresponding charge flowing is given
by
q = it = −
N
R
ϕ
(13.24)
Consider a conducting rod of length l moving sideways in the plane of paper over
a U-shaped metal frame at constant speed v at right angles to a uniform magnetic
field of flux density B into the paper. Then the emf induced across the ends of the
rod is given by
ξ = −Blv
(13.25)
13.2 Problems
13.2.1 Motion of Charged Particles in Electric and Magnetic Fields
13.1 Calculate the cyclotron frequency to accelerate alpha particles in a magnetic
field of 10 4 G. The mass of 4 He 2 is 4.002603 u.
13.2 If the pole pieces of a cyclotron are 50 cm in diameter, a flux density of
15,000 G, find approximate values for the energies to which (a) protons
and (b) α-particles could be accelerated. What oscillator frequency would
be required in each case?
[University of London]
13.3 In a mass spectrometer, the velocity filter employs electric field E and a
perpendicular magnetic field B. The deflection magnetic field, perpendicular
to a beam is B . Ions with similar charges q and mass numbers m 1 and
583
Lenz law: The reason for the minus sign in (13.21) is given by Lenz law which
states ‘the induced current will appear in such a direction that it opposes the change
that produced it’.
If the coil forms a closed circuit then only the induced current can be present,
otherwise in the case of an open circuit one can only speak of induced emf and its
direction.
In a coil of N turns
ξ = −N
ϕ
t
(13.22)
If the circuit is complete current will appear and will be given by
i =
ξ
R
= −
N
R
ϕ
t
(13.23)
where R is the resistance of the circuit. The corresponding charge flowing is given
by
q = it = −
N
R
ϕ
(13.24)
Consider a conducting rod of length l moving sideways in the plane of paper over
a U-shaped metal frame at constant speed v at right angles to a uniform magnetic
field of flux density B into the paper. Then the emf induced across the ends of the
rod is given by
ξ = −Blv
(13.25)
13.2 Problems
13.2.1 Motion of Charged Particles in Electric and Magnetic Fields
13.1 Calculate the cyclotron frequency to accelerate alpha particles in a magnetic
field of 10 4 G. The mass of 4 He 2 is 4.002603 u.
13.2 If the pole pieces of a cyclotron are 50 cm in diameter, a flux density of
15,000 G, find approximate values for the energies to which (a) protons
and (b) α-particles could be accelerated. What oscillator frequency would
be required in each case?
[University of London]
13.3 In a mass spectrometer, the velocity filter employs electric field E and a
perpendicular magnetic field B. The deflection magnetic field, perpendicular
to a beam is B . Ions with similar charges q and mass numbers m 1 and