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3 Consider an aussembles of electrons in a consta magnetic field B = Bx inxtve drrection...
Consider a changing magnetic field (from B′ to B) within a circle of radius 4 m....
Consider a changing magnetic field (from B′ to B) within a
circle of radius 4 m. The magnetic field points into the page ⊗ and
its magnitude is increasing.
The field is defined by B = b t , where b = 0.5 T/s:
A: Find the direction of the induced emf Eind.
1. into the page, 2. out of the page, 3. counter-clockwise, 4.
clockwise
B: Find the magnitude of the induced electric field Eind on the
perimeter of...
3. Electromagnetic Inductance. Consider a single loop under magnetic field. (a) If the area A =...
3. Electromagnetic Inductance. Consider a single loop under magnetic field. (a) If the area A = 0.012[m) is constant, but the magnetic field is increasing at the rate of 0.020 T/s), determine the induced emf. (Use Faraday's law; the induced emf in a loop equals the absolute value of the time rate of change of the magnetic flux through the loop.) (b) If the total resistance of the circuit is 5.0(82), find the induced current. (c) Suppose we change the...
Consider an experimental setup where charged particles (electrons or protons) are first accelerated by an electric field and then injected into a region of constant magnetic field with a field strength of 0.25 T
Consider an experimental setup where charged particles (electrons or protons) are first accelerated by an electric field and then injected into a region of constant magnetic field with a field strength of 0.25 T.Part (a) What is the potential difference, in volts, required in the first part of the experiment to accelerate electrons to a speed of 5.95 x 107 m/s?Part (b) Find the radius of curvature, in meters, of the path of a proton accelerated through this same potential...
7.34 In free space, the magnetic flux density is (a) Show that B is a magnetic field (b) Find the...
7.34 In free space, the magnetic flux density is (a) Show that B is a magnetic field (b) Find the magnetic flux through x-1,0 < 1,1 < z < 4. c) Calculate J (d) Determine the total magnetic flux through the surface of a cube defined by 0 x <2> 0 < y < 2, 0 < z < 2.
7.34 In free space, the magnetic flux density is (a) Show that B is a magnetic field (b) Find the...
Motion of Electrons in a Magnetic Field
An electron of mass m and charge -e is moving through a uniform magnetic field \(\vec{B}=\left(B_{x}, 0,0\right)\)
in vacuum. At the origin, it has velocity \(\vec{v}=\left(v_{x}, v_{y}, 0\right)\), where vx>0 and vy >0. A screen is mounted perpendicular to the x axis at a distance D from the origin.The motion of the electron can be broken down into two parts: 1. constant motion in the x direction plus2. a periodic part, the projection of which in the yz plane is circular. Find the angular...
1-) Show that gyrofrequency of electrons in a uniform magnetic field B is We 2.8 x...
1-) Show that gyrofrequency of electrons in a uniform magnetic field B is We 2.8 x 10 B where fee in Hz and B is in units of G (note that 10 G 1 T). The Earth's magnetic field at the surface is of the order of~0.5 G, show that the corresponding gyrofrequency is MII. ce
3. Assume a three-dimensional space is influenced by a uniform magnetic flux density field B :...
3. Assume a three-dimensional space is influenced by a uniform magnetic flux density field B : R3 R3 such that B(, y, 2)0, 1.5,0]T T [note, the field is uniform because its definition does not depend on the position (x, y, z)]. Consider also three open planar surfaces Sm With m = 1,2,3; each of them has an area of 2 m2. (The periphery of the open surface could be associated with a coil of wire.) The normal vectors of...
Consider an electron in a uniform magnetic field along the z direction. A measurement shows that...
Consider an electron in a uniform magnetic field along the z direction. A measurement shows that the spin is along the negative x direction at -0. a. Find the eigenvector describing the initial spin state. 5. 0 -1 b. Write the Hamiltonian as a 2x2 matrix by starting with H =-7S-Band taking the field B in the z- direction. Find the energy eigenvalues and eigenvectors. Solve for | Ψ(t) using these eigenvalues, eigenvectors, and the initial condition from part a....
1. A magnetic field, 7, propagates in a material with uy = 4 and &r=4 and...
1. A magnetic field, 7, propagates in a material with uy = 4 and &r=4 and is given by H=-v8cos(@t + Bx)+34 cos(@t + Bx). The frequency of operation is 8 GHz. Find: a) the wave number, , b) the phase velocity, vp, c) the intrinsic impedance of the material, n, d) the instantaneous (time domain) expression for the electric field, E.
The force on a charged particle moving in a magnetic field can be computed as the...
The force on a charged particle moving in a magnetic field can be computed as the vector sum of the forces due to each separate component of the magnetic field. As an example, a particle with charge q is moving with speed v in the? y-direction. It is moving in a uniform magnetic field Part A What is the x-component of the force F? exerted on the particle by the magnetic field? Part B What is the y-component of the force...
Consider a changing magnetic field (from B′ to B) within a
circle of radius 4 m. The magnetic field points into the page ⊗ and
its magnitude is increasing.
The field is defined by B = b t , where b = 0.5 T/s:
A: Find the direction of the induced emf Eind.
1. into the page, 2. out of the page, 3. counter-clockwise, 4.
clockwise
B: Find the magnitude of the induced electric field Eind on the
perimeter of...
3. Electromagnetic Inductance. Consider a single loop under magnetic field. (a) If the area A = 0.012[m) is constant, but the magnetic field is increasing at the rate of 0.020 T/s), determine the induced emf. (Use Faraday's law; the induced emf in a loop equals the absolute value of the time rate of change of the magnetic flux through the loop.) (b) If the total resistance of the circuit is 5.0(82), find the induced current. (c) Suppose we change the...
7.34 In free space, the magnetic flux density is (a) Show that B is a magnetic field (b) Find the magnetic flux through x-1,0 < 1,1 < z < 4. c) Calculate J (d) Determine the total magnetic flux through the surface of a cube defined by 0 x <2> 0 < y < 2, 0 < z < 2.
7.34 In free space, the magnetic flux density is (a) Show that B is a magnetic field (b) Find the...
An electron of mass m and charge -e is moving through a uniform magnetic field \(\vec{B}=\left(B_{x}, 0,0\right)\)
in vacuum. At the origin, it has velocity \(\vec{v}=\left(v_{x}, v_{y}, 0\right)\), where vx>0 and vy >0. A screen is mounted perpendicular to the x axis at a distance D from the origin.The motion of the electron can be broken down into two parts: 1. constant motion in the x direction plus2. a periodic part, the projection of which in the yz plane is circular. Find the angular...
1-) Show that gyrofrequency of electrons in a uniform magnetic field B is We 2.8 x 10 B where fee in Hz and B is in units of G (note that 10 G 1 T). The Earth's magnetic field at the surface is of the order of~0.5 G, show that the corresponding gyrofrequency is MII. ce
3. Assume a three-dimensional space is influenced by a uniform magnetic flux density field B : R3 R3 such that B(, y, 2)0, 1.5,0]T T [note, the field is uniform because its definition does not depend on the position (x, y, z)]. Consider also three open planar surfaces Sm With m = 1,2,3; each of them has an area of 2 m2. (The periphery of the open surface could be associated with a coil of wire.) The normal vectors of...
Consider an electron in a uniform magnetic field along the z direction. A measurement shows that the spin is along the negative x direction at -0. a. Find the eigenvector describing the initial spin state. 5. 0 -1 b. Write the Hamiltonian as a 2x2 matrix by starting with H =-7S-Band taking the field B in the z- direction. Find the energy eigenvalues and eigenvectors. Solve for | Ψ(t) using these eigenvalues, eigenvectors, and the initial condition from part a....
1. A magnetic field, 7, propagates in a material with uy = 4 and &r=4 and is given by H=-v8cos(@t + Bx)+34 cos(@t + Bx). The frequency of operation is 8 GHz. Find: a) the wave number, , b) the phase velocity, vp, c) the intrinsic impedance of the material, n, d) the instantaneous (time domain) expression for the electric field, E.
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