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5. [12%) which of the following are local gauge invariant? A. electric field E (YES or...
2 Coulomb Gauge Besides the Lorenz gauge, another typical gauge choice is the Coulomb gauge, defined by a) 2 Points] Is this gauge choice Lorentz invariant, i.e. is it the same for all reference fram...
2 Coulomb Gauge Besides the Lorenz gauge, another typical gauge choice is the Coulomb gauge, defined by a) 2 Points] Is this gauge choice Lorentz invariant, i.e. is it the same for all reference frames? Justify your answer. Hint: It sufices to find a good reasoning here, so you don't necessarily need to compute anything but feel free to do so if you want). b) /2 Points/ Find a condition for x(2) in the Coulomb gauge, such that leaves the...
2 Coulomb Gauge Besides the Lorenz gauge, another typical gauge choice is the Coulomb gauge, defined by a) 2 Points] Is...
2 Coulomb Gauge Besides the Lorenz gauge, another typical gauge choice is the Coulomb gauge, defined by a) 2 Points] Is this gauge choice Lorentz invariant, i.e. is it the same for all reference frames? Justify your answer. Hint: It sufices to find a good reasoning here, so you don't necessarily need to compute anything but feel free to do so if you want). b) /2 Points/ Find a condition for x(2) in the Coulomb gauge, such that leaves the...
Please provide clear steps, I'm a little confused about how to solve this question. Thanks. Problem...
Please provide clear steps, I'm a little confused about how to
solve this question. Thanks.
Problem 2. (20 points) Particle in a magnetic field. The Hamiltonian for a particle of mass m and charge e in arn electronnagnetic field with scalar potential φ(r,t) and vector potential . (r,t) is given by where φ is the scalar potential and A is the vector potential. 2.1. (10 points) Show that the following transformation is canonical for any choice of the parameter o...
how did we get the following equation (1.9) from maxwells equations at e at where p is the density of free charges and j is the density of currents at a point where the electric and magnetic fie...
how
did we get the following equation (1.9) from maxwells
equations
at e at where p is the density of free charges and j is the density of currents at a point where the electric and magnetic fields are evaluated. The parameters and are constants that determine the property of the vacuum and are called the electric permittivity and magnetic permeability respectively The parameter c-1/olo and its numerical value is equal to the speed of light in vacuum,c 3 x...
We know from electrostatics that if we have a scalar electrostatic potential V, then there exists an electric field tha...
We know from electrostatics that if we have a scalar electrostatic potential V, then there exists an electric field that satisfies: Of course, not all vector fields can be written as the gradient of a scalar function. (a) Show that the electric field given below is not the result of an electrostatic potential. E(x, y, z) = ( 3.0m,2 ) ( yi-TJ (b) Just because this electric field can't come from an electrostatic potential, it doesn't mean it can't exist...
4. We know from electrostatics that if we have a scalar electrostatic potential V, then there exists an electric field...
4. We know from electrostatics that if we have a scalar electrostatic potential V, then there exists an electric field that satisfies: Of course, not all vector fields can be written as the gradient of a scalar function. (a) Show that the electric field given below is not the result of an electrostatic potential (b) Just because this electric field can't come from an electrostatic potential, it doesn't mean it can't exist - it just can't be created by static...
B(, t) = Bmar sin(kx - wt). (e) Using Faraday's law, find the electric field induced...
B(, t) = Bmar sin(kx - wt). (e) Using Faraday's law, find the electric field induced by the magnetic wave. (f) In part (e), what is the amplitude of the electric wave? Is there any phase difference between the electric wave and the magnetic wave? (g) The electric field you found in part (e) should also satisfy Ampére-Maxwell equation. Find the speed of the EM wave in terms of the constants en and yo using this requirement.
Question 2: For an electromagnetic plane wave, the electric field is given by: Ē= E, cos(kz...
Question 2: For an electromagnetic plane wave, the electric field is given by: Ē= E, cos(kz +wt) ĉ +0 ġ+02 a) Determine the direction of propagation of the electromagnetic wave. b) Find the magnitude and direction of the magnetic field for the given electromagnetic wave B. c) Calculate the Poynting vector associated with this electromagnetic wave. What direction does this vector point? Does this makes sense? d) If the amplitude of the magnetic field was measured to be 2.5 *...
An electric field is A a scalar function of space B a scalar function of space...
An electric field is A a scalar function of space B a scalar function of space and time C a vector function of space D a vector function of space and time E none of these What about a magnetic field?
Question 2: For an electromagnetic plane wave, the electric field is given by: Ē = E,...
Question 2: For an electromagnetic plane wave, the electric field is given by:$$ \vec{E}=E_{0} \cos (k z+\omega t) \hat{x}+0 \hat{y}+0 \hat{z} $$a) Determine the direction of propagation of the electromagnetic wave.b) Find the magnitude and direction of the magnetic field for the given electromagnetic wave \(\vec{B}\).c) Calculate the Poynting vector associated with this electromagnetic wave. What direction does this vector point? Does this makes sense?d) If the amplitude of the magnetic field was measured to be \(2.5 * 10^{-7} \mathrm{~T}\),...
2 Coulomb Gauge Besides the Lorenz gauge, another typical gauge choice is the Coulomb gauge, defined by a) 2 Points] Is this gauge choice Lorentz invariant, i.e. is it the same for all reference frames? Justify your answer. Hint: It sufices to find a good reasoning here, so you don't necessarily need to compute anything but feel free to do so if you want). b) /2 Points/ Find a condition for x(2) in the Coulomb gauge, such that leaves the...
2 Coulomb Gauge Besides the Lorenz gauge, another typical gauge choice is the Coulomb gauge, defined by a) 2 Points] Is this gauge choice Lorentz invariant, i.e. is it the same for all reference frames? Justify your answer. Hint: It sufices to find a good reasoning here, so you don't necessarily need to compute anything but feel free to do so if you want). b) /2 Points/ Find a condition for x(2) in the Coulomb gauge, such that leaves the...
Please provide clear steps, I'm a little confused about how to
solve this question. Thanks.
Problem 2. (20 points) Particle in a magnetic field. The Hamiltonian for a particle of mass m and charge e in arn electronnagnetic field with scalar potential φ(r,t) and vector potential . (r,t) is given by where φ is the scalar potential and A is the vector potential. 2.1. (10 points) Show that the following transformation is canonical for any choice of the parameter o...
how
did we get the following equation (1.9) from maxwells
equations
at e at where p is the density of free charges and j is the density of currents at a point where the electric and magnetic fields are evaluated. The parameters and are constants that determine the property of the vacuum and are called the electric permittivity and magnetic permeability respectively The parameter c-1/olo and its numerical value is equal to the speed of light in vacuum,c 3 x...
We know from electrostatics that if we have a scalar electrostatic potential V, then there exists an electric field that satisfies: Of course, not all vector fields can be written as the gradient of a scalar function. (a) Show that the electric field given below is not the result of an electrostatic potential. E(x, y, z) = ( 3.0m,2 ) ( yi-TJ (b) Just because this electric field can't come from an electrostatic potential, it doesn't mean it can't exist...
4. We know from electrostatics that if we have a scalar electrostatic potential V, then there exists an electric field that satisfies: Of course, not all vector fields can be written as the gradient of a scalar function. (a) Show that the electric field given below is not the result of an electrostatic potential (b) Just because this electric field can't come from an electrostatic potential, it doesn't mean it can't exist - it just can't be created by static...
B(, t) = Bmar sin(kx - wt). (e) Using Faraday's law, find the electric field induced by the magnetic wave. (f) In part (e), what is the amplitude of the electric wave? Is there any phase difference between the electric wave and the magnetic wave? (g) The electric field you found in part (e) should also satisfy Ampére-Maxwell equation. Find the speed of the EM wave in terms of the constants en and yo using this requirement.
Question 2: For an electromagnetic plane wave, the electric field is given by: Ē= E, cos(kz +wt) ĉ +0 ġ+02 a) Determine the direction of propagation of the electromagnetic wave. b) Find the magnitude and direction of the magnetic field for the given electromagnetic wave B. c) Calculate the Poynting vector associated with this electromagnetic wave. What direction does this vector point? Does this makes sense? d) If the amplitude of the magnetic field was measured to be 2.5 *...
An electric field is A a scalar function of space B a scalar function of space and time C a vector function of space D a vector function of space and time E none of these What about a magnetic field?
Question 2: For an electromagnetic plane wave, the electric field is given by:$$ \vec{E}=E_{0} \cos (k z+\omega t) \hat{x}+0 \hat{y}+0 \hat{z} $$a) Determine the direction of propagation of the electromagnetic wave.b) Find the magnitude and direction of the magnetic field for the given electromagnetic wave \(\vec{B}\).c) Calculate the Poynting vector associated with this electromagnetic wave. What direction does this vector point? Does this makes sense?d) If the amplitude of the magnetic field was measured to be \(2.5 * 10^{-7} \mathrm{~T}\),...
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