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Calculate the frequency at which the conduction and displacement currents become equal with unity conductivity in a material of permittivity 2.
To find the frequency at which the conduction current ((I_c)) and displacement current ((I_d)) become equal in a material, we first need to understand the equations governing these currents in relation to the material's properties.The conduction current density ((J_c)) is given by Ohm's law:[J_c = sRead more
To find the frequency at which the conduction current ((I_c)) and displacement current ((I_d)) become equal in a material, we first need to understand the equations governing these currents in relation to the material’s properties.
The conduction current density ((J_c)) is given by Ohm’s law:
[J_c = sigma E]
where (sigma) is the conductivity of the material and (E) is the electric field.
The displacement current density ((J_d)) can be described in relation to the changing electric field as:
[J_d = epsilon frac{dE}{dt}]
where (epsilon) is the permittivity of the material, and (frac{dE}{dt}) represents the rate of change of the electric field with respect to time.
Given that (sigma = 1) S/m (unity conductivity) and (epsilon = 2), to find the frequency ((f)) at which (J_c = J_d), set the expressions for (J_c) and (J_d) equal to each other and solve for (f).
[J_c = J_d]
[sigma E = epsilon frac{dE}{dt}]
Because we’re concerned with frequencies, a useful form of (E) to consider is one that oscillates sinusoidally, so let (E = E_0 sin(
See lessFind the magnitude of the displacement current density in air at a frequency of 18GHz in frequency domain. Take electric field E as 4 units.
To find the magnitude of the displacement current density ((J_d)) in air for a given frequency, you use the relation for displacement current density in the frequency domain, which is given by the formula[ J_d = jomegaepsilon E ]Where:- (J_d) is the displacement current density.- (j) represents theRead more
To find the magnitude of the displacement current density ((J_d)) in air for a given frequency, you use the relation for displacement current density in the frequency domain, which is given by the formula
[ J_d = jomegaepsilon E ]
Where:
– (J_d) is the displacement current density.
– (j) represents the imaginary unit (sqrt(-1)).
– (omega) is the angular frequency, obtained from (2pi f), with (f) being the frequency in hertz.
– (epsilon) is the permittivity of the medium (for air, it’s close to the permittivity of free space (epsilon_0 = 8.854 times 10^{-12} F/m)).
– (E) is the magnitude of the electric field.
Given:
– Frequency, (f = 18 , GHz = 18 times 10^9 , Hz)
– Electric field, (E = 4) units.
First, calculate (omega):
[ omega = 2pi f = 2pi times 18 times 10^9 ]
[ omega approx 113.1 times 10^9 , rad/s ]
Now, substitute (omega), (E), and (epsilon_0) into the (J_d) formula:
[ J_d = jomega
See lessCalculate the displacement current density when the electric flux density is 20sin 0.5t.
To calculate the displacement current density ((J_d)) when the electric flux density ((D)) is given by (D = 20sin(0.5t)), we'll make use of Maxwell's displacement current concept. The displacement current density can be found using the equation:[J_d = frac{dD}{dt}]Given that (D = 20sin(0.5t)), let'sRead more
To calculate the displacement current density ((J_d)) when the electric flux density ((D)) is given by (D = 20sin(0.5t)), we’ll make use of Maxwell’s displacement current concept. The displacement current density can be found using the equation:
[
J_d = frac{dD}{dt}
]
Given that (D = 20sin(0.5t)), let’s differentiate it with respect to (t):
[
frac{dD}{dt} = 20cos(0.5t) times 0.5 = 10cos(0.5t)
]
So, the displacement current density, (J_d), is:
[
J_d = 10cos(0.5t)
]
This expression provides the displacement current density as a function of time.
See lessFind the conductivity of a material with conduction current density 100 units and electric field of 4 units.
The conductivity ((sigma)) of a material can be found using the relation between the conduction current density ((J)), the electric field ((E)), and the conductivity itself. The relation is given by Ohm's Law in its differential form:[ J = sigma E ]Given:- (J = 100) units (Conduction current densityRead more
The conductivity ((sigma)) of a material can be found using the relation between the conduction current density ((J)), the electric field ((E)), and the conductivity itself. The relation is given by Ohm’s Law in its differential form:
[ J = sigma E ]
Given:
– (J = 100) units (Conduction current density)
– (E = 4) units (Electric field)
To find the conductivity ((sigma)), we rearrange the equation:
[ sigma = frac{J}{E} ]
Substituting the given values:
[ sigma = frac{100}{4} = 25 ]
Therefore, the conductivity of the material is 25 units.
See lessFind the velocity of an electron when its kinetic energy is equal to one electron volt (in 10 5 m/s). Given charge of an electron e = 1.6 x 10 -19 and mass of an electron m = 9.1 x 10
To find the velocity of an electron when its kinetic energy (K) is equal to 1 electron volt (eV), we use the relation between kinetic energy and velocity, and the given values for the charge (e) and mass (m) of an electron.The kinetic energy K in joules for an electron can be given by the equation (Read more
To find the velocity of an electron when its kinetic energy (K) is equal to 1 electron volt (eV), we use the relation between kinetic energy and velocity, and the given values for the charge (e) and mass (m) of an electron.
The kinetic energy K in joules for an electron can be given by the equation ( K = frac{1}{2} mv^2 ), where (m) is the mass of the electron and (v) is its velocity.
Given:
– (K = 1 , text{eV} = 1.6 times 10^{-19} , text{J}) (since (1 , text{eV} = 1.6 times 10^{-19} , text{J}))
– (m = 9.1 times 10^{-31} , text{kg})
– (e = 1.6 times 10^{-19} , text{C}) (charge of the electron, although it’s not directly used in the calculation for velocity, it’s useful for understanding the energy conversion)
Starting with the relationship between kinetic energy and velocity:
[ K = frac{1}{2} mv^2 ]
Solving for (v):
[ v = sqrt{frac{2K}{m}} ]
Plugging in the values:
[ v =
See lessFind the mean free path of an electron travelling at a speed of 18m/s in 2 seconds.
To find the mean free path of an electron traveling at a speed of (18 , text{m/s}) in (2 , text{seconds}), we need to understand what mean free path is first. The mean free path is the average distance traveled by a moving particle (such as an electron) between successive impacts (collisions), whichRead more
To find the mean free path of an electron traveling at a speed of (18 , text{m/s}) in (2 , text{seconds}), we need to understand what mean free path is first. The mean free path is the average distance traveled by a moving particle (such as an electron) between successive impacts (collisions), which modify its direction or energy or other particle properties. However, to calculate the mean free path directly from the information provided (speed and time) without details about the frequency or probability of collisions, or the specifics of the medium the electron is moving through (like its density or the cross-sectional area for collision), is not straightforward.
Given the velocity of the electron ((v = 18 , text{m/s})) and the time ((t = 2 , text{s})), you might be looking for the distance traveled rather than the mean free path per se, as the actual calculation of mean free path requires statistical mechanics and knowledge of the conditions (like pressure and temperature for gases or the material properties for solids or liquids).
However, if we interpret your question as seeking the distance traveled under the assumption that this distance is a proxy for the “mean free path” in a very idealized context where every 2 seconds the electron’s path is somehow altered, here’s a simple calculation:
Distance traveled, (d = vt), where (v = 18 , text{m
See lessThe superconducting materials will be independent of which of the following?
The superconducting materials will be independent of external magnetic field strength up to a critical limit. Beyond this critical magnetic field strength, superconductivity is destroyed. Superconductivity is also independent of normal resistive mechanisms present in conventional conductors but depeRead more
The superconducting materials will be independent of external magnetic field strength up to a critical limit. Beyond this critical magnetic field strength, superconductivity is destroyed. Superconductivity is also independent of normal resistive mechanisms present in conventional conductors but depends on factors like temperature, magnetic field, and material purity.
See lessThe magnetic susceptibility in a superconductor will be
The magnetic susceptibility in a superconductor will be -1.
The magnetic susceptibility in a superconductor will be -1.
See lessThe magnetic field which destroys the superconductivity is called
The magnetic field which destroys the superconductivity is called the critical magnetic field.
The magnetic field which destroys the superconductivity is called the critical magnetic field.
See lessFor a dielectric which of the following properties hold good?
For a dielectric, the following properties generally hold good: 1. Polarization: When a dielectric is placed in an external electric field, it becomes polarized. This means that the centers of positive and negative charges within the material shift slightly, creating an internal electric field thatRead more
For a dielectric, the following properties generally hold good:
1. Polarization: When a dielectric is placed in an external electric field, it becomes polarized. This means that the centers of positive and negative charges within the material shift slightly, creating an internal electric field that opposes the external one.
2. Dielectric Constant: Also known as the relative permittivity, this is a measure of how much the electric field in the dielectric is reduced compared to a vacuum. A higher dielectric constant indicates a material that more effectively reduces the field.
3. Dielectric Strength: This is the maximum electric field that a dielectric can withstand without undergoing electrical breakdown (where it becomes conductive). Dielectric strength is usually given in Volts per unit thickness (like kV/mm).
4. Energy Storage: A dielectric material can store electrical energy by means of the polarization of its molecules. This property is utilized in capacitors, where dielectric materials are used to increase the energy storage capacity.
5. Non-conductivity: Ideally, a dielectric material does not conduct electric current, as it is an insulator. However, at very high electric fields (beyond the dielectric strength), dielectric breakdown can occur, and the material may become conductive.
6. Frequency Dependence: The dielectric properties of a material can depend on the frequency of the applied electric field. For example, the dielectric constant can decrease with increasing frequency
See less