644
14 Electromagnetism II
S ave =
E 2
0
2μ 0 c
[University of Durham 2003]
14.51 A plane electromagnetic wave has E x = E y = 0 and
E z = 50 sin
4π ×10 14
t −
x
3×10 8
. Calculate the irradiance (flux density).
14.52 Show that E × H is in the same direction as the wave propagates and has
magnitude equal to |E × H| =
|E| 2
μ 0 c .
[University of Aberystwyth, Wales]
14.53 An electromagnetic plane wave in vacuum has E-field given by
E z = 10 sin π(2 × 10
6 x − 6 × 10
14 t), E x = E y = 0.
Find (a) frequency; (b) wavelength; (c) speed; (d) E-field amplitude;
(e) polarization.
14.54 Write down the equation for the associated magnetic field for the wave given
in prob. (14.53).
14.55 A radar monitors the speed v of approaching cars by sending out waves of
frequency ν. If the frequency received is ν , find the speed of the car. How
would the beat frequency change if the car is receding?
14.56 Microwaves of frequency 800 MHz are beamed by a stationary police man
towards a receding car speeding at 90 km/h. What beat frequency was registered by the radar?
14.57 State Ampere’s law.
A long solid conductor of radius a lies on the axis of a long cylinder of
inner radius b and outer radius c. The central conductor carries a current i
while the outer conductor carries a current −i. The currents are uniformly
distributed over the cross-sections of each conductor. By considering the
current enclosed by a circular loop of radius r centred on the axis of the
inner conductor use Ampere’s law to calculate the magnetic field in each of
the four regions (a) r < a, (b) a < r < b, (c) b < r < c, (d) r > c.
14.58 The CMS experiment at the Large Hadron Collider at CERN uses a large,
cylindrical, superconducting solenoid. This magnet is 12.5 m in length with
a diameter of 6 m. When powered, it generates a uniform magnetic field of
4 T. Estimate the energy stored in the magnetic field.
14.59 Given that the total power radiated by the sun in the form of electromagnetic
radiation is 4 × 10 26 W, estimate the electric and magnetic field amplitude at
the surface of the sun. (The radius of the sun is 7 × 10 8 m).
[University of Durham 2003]
14 Electromagnetism II
S ave =
E 2
0
2μ 0 c
[University of Durham 2003]
14.51 A plane electromagnetic wave has E x = E y = 0 and
E z = 50 sin
4π ×10 14
t −
x
3×10 8
. Calculate the irradiance (flux density).
14.52 Show that E × H is in the same direction as the wave propagates and has
magnitude equal to |E × H| =
|E| 2
μ 0 c .
[University of Aberystwyth, Wales]
14.53 An electromagnetic plane wave in vacuum has E-field given by
E z = 10 sin π(2 × 10
6 x − 6 × 10
14 t), E x = E y = 0.
Find (a) frequency; (b) wavelength; (c) speed; (d) E-field amplitude;
(e) polarization.
14.54 Write down the equation for the associated magnetic field for the wave given
in prob. (14.53).
14.55 A radar monitors the speed v of approaching cars by sending out waves of
frequency ν. If the frequency received is ν , find the speed of the car. How
would the beat frequency change if the car is receding?
14.56 Microwaves of frequency 800 MHz are beamed by a stationary police man
towards a receding car speeding at 90 km/h. What beat frequency was registered by the radar?
14.57 State Ampere’s law.
A long solid conductor of radius a lies on the axis of a long cylinder of
inner radius b and outer radius c. The central conductor carries a current i
while the outer conductor carries a current −i. The currents are uniformly
distributed over the cross-sections of each conductor. By considering the
current enclosed by a circular loop of radius r centred on the axis of the
inner conductor use Ampere’s law to calculate the magnetic field in each of
the four regions (a) r < a, (b) a < r < b, (c) b < r < c, (d) r > c.
14.58 The CMS experiment at the Large Hadron Collider at CERN uses a large,
cylindrical, superconducting solenoid. This magnet is 12.5 m in length with
a diameter of 6 m. When powered, it generates a uniform magnetic field of
4 T. Estimate the energy stored in the magnetic field.
14.59 Given that the total power radiated by the sun in the form of electromagnetic
radiation is 4 × 10 26 W, estimate the electric and magnetic field amplitude at
the surface of the sun. (The radius of the sun is 7 × 10 8 m).
[University of Durham 2003]