vacuum the following relations hold:
aE
OB OB
aE
2
at
ax
at
ar
4.196. Find the mean Poynting vector (8) of a plane electromagnetic wave E = Em cos (cot — kr) if the wave propagates in vacuum.
4.197.. A plane harmonic electromagnetic wave with plane polarization propagates in vacuum. The electric component of the wave
has a strength amplitude En, = 50 mV/m, the frequency is v
100 MHz. Find:
(a) the efficient value of the displacement current density;
(b) the mean energy flow density averaged over an oscillation
period.
4.198. A ball of radius /I = 50 cm is located in a non-magnetic
medium with permittivity a = 4.0. In that medium a plane electromagnetic wave propagates,the strength amplitude of whose electric
component is equal to Eni, = 200 Vim. What amount of energy
reaches the ball during a time interval t = 1.0 min?
4.199. A standing electromagnetic wave with electric component
E = Em cos kx•cos cot is sustained along the x axis in vacuum. Find
the magnetic component of the wave B (x, t). Draw the approximate
distribution pattern of the wave's electric and magnetic components
(E and B) at the moments t = 0 and t = T/4, where T is the oscillation period.
4.200. A standing electromagnetic wave E = Em cos kx• cos cot
is sustained along the x axis in vacuum. Find the projection of the
Poynting vector on the x axis
(x, t) and the mean value of that
projection averaged over an oscillation period.
4.201. A parallel-plate air capacitor whose electrodes are shaped
as discs of radius R = 6.0 cm is connected to a source of an alternating sinusoidal voltage with frequency co = 1000 s-1. Find the
ratio of peak values of magnetic and electric energies within the
capacitor.
4.202. An alternating sinusoidal current of frequency co
1000 s-1 flows in the winding of a straight solenoid whose crosssectional radius is equal to R = 6.0 cm. Find the ratio of peak
values of electric and magnetic energies within the solenoid.
4.203. A parallel-plate capacity whose electrodes are shaped as
round discs is charged slowly. Demonstrate that the flux of the
Poynting vector across the capacitor's lateral surface is equal to the
increment of the capacitor's energy per unit time. The dissipation
of field at the edge is to be neglected in calculations.
4.204. A current I flows along a straight conductor with round
cross-section. Find the flux of the Poynting vector across the lateral
surface of the conductor's segment with resistance R.
4.205. Non-relativistic protons accelerated by a potential difference U form a round beam with current I. Find the magnitude and
13*
195
aE
OB OB
aE
2
at
ax
at
ar
4.196. Find the mean Poynting vector (8) of a plane electromagnetic wave E = Em cos (cot — kr) if the wave propagates in vacuum.
4.197.. A plane harmonic electromagnetic wave with plane polarization propagates in vacuum. The electric component of the wave
has a strength amplitude En, = 50 mV/m, the frequency is v
100 MHz. Find:
(a) the efficient value of the displacement current density;
(b) the mean energy flow density averaged over an oscillation
period.
4.198. A ball of radius /I = 50 cm is located in a non-magnetic
medium with permittivity a = 4.0. In that medium a plane electromagnetic wave propagates,the strength amplitude of whose electric
component is equal to Eni, = 200 Vim. What amount of energy
reaches the ball during a time interval t = 1.0 min?
4.199. A standing electromagnetic wave with electric component
E = Em cos kx•cos cot is sustained along the x axis in vacuum. Find
the magnetic component of the wave B (x, t). Draw the approximate
distribution pattern of the wave's electric and magnetic components
(E and B) at the moments t = 0 and t = T/4, where T is the oscillation period.
4.200. A standing electromagnetic wave E = Em cos kx• cos cot
is sustained along the x axis in vacuum. Find the projection of the
Poynting vector on the x axis
(x, t) and the mean value of that
projection averaged over an oscillation period.
4.201. A parallel-plate air capacitor whose electrodes are shaped
as discs of radius R = 6.0 cm is connected to a source of an alternating sinusoidal voltage with frequency co = 1000 s-1. Find the
ratio of peak values of magnetic and electric energies within the
capacitor.
4.202. An alternating sinusoidal current of frequency co
1000 s-1 flows in the winding of a straight solenoid whose crosssectional radius is equal to R = 6.0 cm. Find the ratio of peak
values of electric and magnetic energies within the solenoid.
4.203. A parallel-plate capacity whose electrodes are shaped as
round discs is charged slowly. Demonstrate that the flux of the
Poynting vector across the capacitor's lateral surface is equal to the
increment of the capacitor's energy per unit time. The dissipation
of field at the edge is to be neglected in calculations.
4.204. A current I flows along a straight conductor with round
cross-section. Find the flux of the Poynting vector across the lateral
surface of the conductor's segment with resistance R.
4.205. Non-relativistic protons accelerated by a potential difference U form a round beam with current I. Find the magnitude and
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195