13.3 Solutions
599
(iii) Obtain an expression for the emf induced in the coil if the wire is placed
at x = b/4 and the current varies with time according to I = 2t.
13.83 Show that in the betatron the magnetic flux ∅ linking an electron orbit of
radius R is given instantaneously by ∅ = 2π R 2 B where B is the instantaneous magnetic field.
[University of Newcastle upon Tyne 1965]
13.2.6 Hall Effect
13.84 What is the Hall effect and what is the significance of a positive Hall coefficient?
A potential difference is applied between the ends of a strip of copper and
a current of 100 A flows along its length. The strip is 20 cm long in the
x-direction of a rectangular system of coordinates, 2 cm wide in the ydirection and 1 mm thick in the z-direction. A uniform magnetic field of
10 Wb/m 2 is applied across the strip in the positive y- direction and the hall
EMF is found to be 5 μV
Derive (a) the magnitude and direction of the Hall field when the current
flows in the positive x-direction and (b) the concentration of free electrons.
[University of Manchester 1972]
13.85 The Hall coefficient and electrical conductivity of an n-type silicon are
−7.3×10 −5 m 3 /C and 2×10 7 mho/m, respectively. Calculate the magnitude
of the mobility of the electrons.
[University of Durham 1962]
13.3 Solutions
13.3.1 Motion of Charged Particles in Electric and Magnetic Fields
13.1 10
4 G = 1 T
f =
Bq
2π m
=
1 × 1.6 × 10 −19
2π × 4.0026 × 1.66 × 10 −27 = 3.83 × 10
6 Hz = 3.83 MHz
13.2 (a) K p =
1
2
q 2 r 2 B 2
m p
=
1
2
×
(1.6 × 10 −19 ) 2 (0.25) 2 (1.5) 2
1.66 × 10 −27
= 2.17 × 10
−13 J =
2.17 × 10 −12
1.6 × 10 −13 MeV = 13.56 MeV
599
(iii) Obtain an expression for the emf induced in the coil if the wire is placed
at x = b/4 and the current varies with time according to I = 2t.
13.83 Show that in the betatron the magnetic flux ∅ linking an electron orbit of
radius R is given instantaneously by ∅ = 2π R 2 B where B is the instantaneous magnetic field.
[University of Newcastle upon Tyne 1965]
13.2.6 Hall Effect
13.84 What is the Hall effect and what is the significance of a positive Hall coefficient?
A potential difference is applied between the ends of a strip of copper and
a current of 100 A flows along its length. The strip is 20 cm long in the
x-direction of a rectangular system of coordinates, 2 cm wide in the ydirection and 1 mm thick in the z-direction. A uniform magnetic field of
10 Wb/m 2 is applied across the strip in the positive y- direction and the hall
EMF is found to be 5 μV
Derive (a) the magnitude and direction of the Hall field when the current
flows in the positive x-direction and (b) the concentration of free electrons.
[University of Manchester 1972]
13.85 The Hall coefficient and electrical conductivity of an n-type silicon are
−7.3×10 −5 m 3 /C and 2×10 7 mho/m, respectively. Calculate the magnitude
of the mobility of the electrons.
[University of Durham 1962]
13.3 Solutions
13.3.1 Motion of Charged Particles in Electric and Magnetic Fields
13.1 10
4 G = 1 T
f =
Bq
2π m
=
1 × 1.6 × 10 −19
2π × 4.0026 × 1.66 × 10 −27 = 3.83 × 10
6 Hz = 3.83 MHz
13.2 (a) K p =
1
2
q 2 r 2 B 2
m p
=
1
2
×
(1.6 × 10 −19 ) 2 (0.25) 2 (1.5) 2
1.66 × 10 −27
= 2.17 × 10
−13 J =
2.17 × 10 −12
1.6 × 10 −13 MeV = 13.56 MeV