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A. If B (1)-9B1şinωt = ỹ3X 10-6sǐlWt Tesla is the field aftertipping to the xy-plane (φ π/2) 1. W...
1. Consider a curve C in the xy-plane given in polar form by r 2 =...
1. Consider a curve C in the xy-plane given in polar form by r 2 = sin(2θ). (a) (3 points) Draw the graph of C. Particularly, be clear in showing the tangent lines to C at the pole. [Hint. The period is π.] (b) (2 points) Compute the area of the region inside C
2 2 Зу The electric potential at points in an xy plane is given by V...
2 2 Зу The electric potential at points in an xy plane is given by V = 2x What are the magnitude and direction of the electric field at the point (3, 2) in meters? Select one: a. -12 with angle 30° b. -12 with angle 60° C.-12 with angle 135° d. 17 with angle 35 e. 17 with angle 65 O f. 17 with angle 135
The electric field in the xy-plane due to an infinite line of charge along the z-axis...
The electric field in the xy-plane due to an infinite line of charge along the z-axis is a gradient field with a potential function V(x,y) = c In To 2 + y2 where c> 0 is a constant and ro is a reference distance at which the potential is assumed to be 0. Use this information to answer parts a through c. a. Find the components of the electric field in the x- and y-directions, where E(x,y)= - VV(x,y). Choose...
An object is moving in the xy-plane and its position after t-seconds is r(t)-t 2, t2...
An object is moving in the xy-plane and its position after t-seconds is r(t)-t 2, t2 - 2t>. (a) Find the position of the object at time t-5. C 3 15 (b) At what time is the object at the point (O, 0)? t- (c) Does the object pass through the point (4, 28)? Yes 0 No (d) Find an equation in x and y whose graph is the path of the object.
(3) A uniform field varies according to B() 4.0+20+0.5 2 (B is in tesla and t...
(3) A uniform field varies according to B() 4.0+20+0.5 2 (B is in tesla and t in seconds). A wire loop with sides of length 4 cm is present as shown. I (a) What is the direction of the induced current in the loop? (b) What is the induced EMF in the loop at t - 0 s? What is the current? (c) What is the EMF and current at t-10 s? Two rods (shown in black in the figure)...
2. (25 points). Rabi oscillations. Consider a spin-1/2 particle in a magnetic field B - Bo2 such ...
2. (25 points). Rabi oscillations. Consider a spin-1/2 particle in a magnetic field B - Bo2 such that the spin eigenstates are split in energy by hwo (let's label the ground state |0) and the excited state |1)). The Hamiltonian for the system is written as hwo Zeeman - _ here and below. ơng,z are the usual Pauli matrices. A second, oscillating field is applied in the transverse plane, giving rise to a time-dependent term in the Hamiltoniain hw Rabi-...
1. 2. 6. 4. Vectors A and B lie in an xy plane. A has magnitude...
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Vectors A and B lie in an xy plane. A has magnitude 5.2 and angle 121°; B has components B - -8.80 and By - -5.09. (a) What is 5A-B ? what is 4A x 38 in unit-vector notation ((b), (c) and (d) for i , j and k components respectively)? (e) what is the angle between the directions of A and 4A x 38 7 what is A + 3.00k in unit-vector notation (), (a)...
3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vec...
3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vector field F(x.y)-(r-yi+r+y)j and the circle C: r y-9. Verify Green's Theorem by calculating the outward flux of F across C (12 points) Find the absolute extreme values of the function .-2-4--3 on the closed triangular region in the xy-plane bounded by the lines x...
Problem 31: (34 points) 1. (10 points) A pulse width modulated (PWM) signal fPwM(t) in Figure...
Problem 31: (34 points) 1. (10 points) A pulse width modulated (PWM) signal fPwM(t) in Figure 2. The symbol D represents a duty cycle, a number between zero and one. Determine the compact trigonometric Fourier series coefficients (Co C,11 %) of the signal f(t). 2. (10 points) One use of PWM is to generate variable DC voltages. While the PWM signal is not DC, you should be able to see from your results in part 1 that it hss a...
Help with question 2 1. what is the electric field at the centre (r = 0)...
Help with question 2
1. what is the electric field at the centre (r = 0) of a hemisphere bounded by r = a, 0 < θ < π/2 and 0 < φ < 2m, that carries a uniform volumetric charge density P3(The charges are distributed in this hemispherical 3D space. Use spherical coordinates due to the hemispherical geometry.) Consider some charges that are lined up in a straight line. This line of charge carries a uniform linear charge density....
2 2 Зу The electric potential at points in an xy plane is given by V = 2x What are the magnitude and direction of the electric field at the point (3, 2) in meters? Select one: a. -12 with angle 30° b. -12 with angle 60° C.-12 with angle 135° d. 17 with angle 35 e. 17 with angle 65 O f. 17 with angle 135
The electric field in the xy-plane due to an infinite line of charge along the z-axis is a gradient field with a potential function V(x,y) = c In To 2 + y2 where c> 0 is a constant and ro is a reference distance at which the potential is assumed to be 0. Use this information to answer parts a through c. a. Find the components of the electric field in the x- and y-directions, where E(x,y)= - VV(x,y). Choose...
An object is moving in the xy-plane and its position after t-seconds is r(t)-t 2, t2 - 2t>. (a) Find the position of the object at time t-5. C 3 15 (b) At what time is the object at the point (O, 0)? t- (c) Does the object pass through the point (4, 28)? Yes 0 No (d) Find an equation in x and y whose graph is the path of the object.
(3) A uniform field varies according to B() 4.0+20+0.5 2 (B is in tesla and t in seconds). A wire loop with sides of length 4 cm is present as shown. I (a) What is the direction of the induced current in the loop? (b) What is the induced EMF in the loop at t - 0 s? What is the current? (c) What is the EMF and current at t-10 s? Two rods (shown in black in the figure)...
2. (25 points). Rabi oscillations. Consider a spin-1/2 particle in a magnetic field B - Bo2 such that the spin eigenstates are split in energy by hwo (let's label the ground state |0) and the excited state |1)). The Hamiltonian for the system is written as hwo Zeeman - _ here and below. ơng,z are the usual Pauli matrices. A second, oscillating field is applied in the transverse plane, giving rise to a time-dependent term in the Hamiltoniain hw Rabi-...
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Vectors A and B lie in an xy plane. A has magnitude 5.2 and angle 121°; B has components B - -8.80 and By - -5.09. (a) What is 5A-B ? what is 4A x 38 in unit-vector notation ((b), (c) and (d) for i , j and k components respectively)? (e) what is the angle between the directions of A and 4A x 38 7 what is A + 3.00k in unit-vector notation (), (a)...
3) (11 points) Consider the vector field Use the Fundamental Theorem of lLine Integrals to find the work done by F along any curve from 41. 1Le) to B(2. el) 4) (10 points) Consider the vector field F(x.y)-(r-yi+r+y)j and the circle C: r y-9. Verify Green's Theorem by calculating the outward flux of F across C (12 points) Find the absolute extreme values of the function .-2-4--3 on the closed triangular region in the xy-plane bounded by the lines x...
Problem 31: (34 points) 1. (10 points) A pulse width modulated (PWM) signal fPwM(t) in Figure 2. The symbol D represents a duty cycle, a number between zero and one. Determine the compact trigonometric Fourier series coefficients (Co C,11 %) of the signal f(t). 2. (10 points) One use of PWM is to generate variable DC voltages. While the PWM signal is not DC, you should be able to see from your results in part 1 that it hss a...
Help with question 2
1. what is the electric field at the centre (r = 0) of a hemisphere bounded by r = a, 0 < θ < π/2 and 0 < φ < 2m, that carries a uniform volumetric charge density P3(The charges are distributed in this hemispherical 3D space. Use spherical coordinates due to the hemispherical geometry.) Consider some charges that are lined up in a straight line. This line of charge carries a uniform linear charge density....
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