13.2 Problems
587
13.20 Electrons are liberated with zero velocity from the negative plate of a parallel
plate condenser, in which there is a constant magnetic field B parallel to the
plates. If the separation of the plates is d and the potential across them is V ,
show that the electrons only arrive at the positive plate if d 2 <
2mV
eB 2
[University of Durham 1962]
13.2.2 Magnetic Induction
13.21 The magnetic field at 40 cm from a long straight wire is 10 −6 T. What current
is carried by the wire?
13.22 A current I flows through a straight wire AB of finite length.
(a) Find the magnetic field B at distance r from the wire, the ends of the
wire making inner angles θ 1 and θ 2 with P, Fig. 13.3.
(b) Obtain the limit value for B for a very long wire.
Fig. 13.3
13.23 The magnetic field at the centre of a circular current loop is 10 −5 T. If the
radius of the loop is 50 cm, find the current.
13.24 A square conducting loop, of side a carries a current I . Calculate the magnetic field at the centre of the loop.
13.25 Two wires are bent into semicircles of radius a, as in Fig. 13.4. The upper
half has resistance R and the lower half resistance 4R . Find the magnetic
induction at the centre of the circle.
Fig. 13.4
587
13.20 Electrons are liberated with zero velocity from the negative plate of a parallel
plate condenser, in which there is a constant magnetic field B parallel to the
plates. If the separation of the plates is d and the potential across them is V ,
show that the electrons only arrive at the positive plate if d 2 <
2mV
eB 2
[University of Durham 1962]
13.2.2 Magnetic Induction
13.21 The magnetic field at 40 cm from a long straight wire is 10 −6 T. What current
is carried by the wire?
13.22 A current I flows through a straight wire AB of finite length.
(a) Find the magnetic field B at distance r from the wire, the ends of the
wire making inner angles θ 1 and θ 2 with P, Fig. 13.3.
(b) Obtain the limit value for B for a very long wire.
Fig. 13.3
13.23 The magnetic field at the centre of a circular current loop is 10 −5 T. If the
radius of the loop is 50 cm, find the current.
13.24 A square conducting loop, of side a carries a current I . Calculate the magnetic field at the centre of the loop.
13.25 Two wires are bent into semicircles of radius a, as in Fig. 13.4. The upper
half has resistance R and the lower half resistance 4R . Find the magnetic
induction at the centre of the circle.
Fig. 13.4