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The electrostatic potential in a particular xy coordinate system is given by V(x,y)- 3xy 5y 2....
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...
The electrostatic potential is V(x.y, z) = a(x2- y2). What are the SI units for the...
The electrostatic potential is V(x.y, z) = a(x2- y2). What are the SI units for the constant a? Calculate: (a) the electric field E: (b) Vx E; Is Va possible electrostatic potential?; (c) the charge density p: (d) the energy density.
11. Consider the parabolic coordinate system (u, v) related to the Cartesian coordi- nates (r, y)...
11. Consider the parabolic coordinate system (u, v) related to the Cartesian coordi- nates (r, y) by х — 2иv, y — u? — u? for (и, v) € [0, оо) х [0, оо) 1 u = 1, u 2' (a) Sketch in the ry-plane the curves given u = 2. Then sketch in 1 v = 1, v = 2. Shade in the region R the xy-plane the curves given v = 2' bounded by the curves given by...
The equation of electric potential in space is given by: V(x,y,z) = 2xy/x 1. Calculate the...
The equation of electric potential in space is given by: V(x,y,z) = 2xy/x 1. Calculate the electric potential at point (x = 1, y = -2, z = 3) in space. 2. Find the electric field E vector as a function of x, y, z. 3. Calculate the electric field at point (x = 1, y = -2, z = 3) in space.
Given the velocity potential for a 2-D incompressible flow, (x, y) = xy + x2 -...
Given the velocity potential for a 2-D incompressible flow, (x, y) = xy + x2 - y2 (a) Does the potential satisfy the Laplace Equation (i.e. V20 = 0)? What is the physical intepretation of this? (b) Find u(x,y) and v(x,y) (the corresponding velocity field of the flow). (c) Does the stream function y (x,y) exist? If so: (a) Find the stream function. (b) Find the implicit equation of streamline that passes through (x,y) = (1, 2).
6. You are in a region of space where the electric potential is given by: V(x,y,z)...
6. You are in a region of space where the electric potential is given by: V(x,y,z) Voxy2ln(z) f for all points where z-0 (above the x-y plane)) Find an expression for the electric field Е(x, y, z). State this vectorially.
The electric potential depends on x and y as shown, for the coordinate axes, in the...
The electric potential depends on x and y as shown, for the
coordinate axes, in the figure (the potential does not depend on
z). The scale of the vertical axis is set by Vs = 500 V. What is
the direction of the electric field?
0.2 V (V) o'z od x(m) y (m)
(9 marks) QUESTION 4 a) Given vector field Éx,y,z) --yº coszi - 3xy cosz j+ xy"...
(9 marks) QUESTION 4 a) Given vector field Éx,y,z) --yº coszi - 3xy cosz j+ xy" sinzk. Show that F is a conservative vector field. (4 marks) ii) Find the potential function, f such that F=Vf. (4 marks)
Given the potential V=x^yz2 [V] find the electric field E at (x 1,y=2,z=1 (i) (ii) calculate...
Given the potential V=x^yz2 [V] find the electric field E at (x 1,y=2,z=1 (i) (ii) calculate the work done in moving a 2 uC charge from A-(1,1,1) to B-(4,-1,1)
Please show work!! (1 point) Take the system x' = 4x – xy, y = 5y...
Please show work!!
(1 point) Take the system x' = 4x – xy, y = 5y + x2. How many critical points are there? What is the critical point with the largest x-coordinate? ( The linearization at this point is | tion at this point is [*] =A (Where A is where A is ul A = At this point the behavior is For behavior write one of "saddle", "source", "sink", "spiral sink", "spiral source", "center".
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...
The electrostatic potential is V(x.y, z) = a(x2- y2). What are the SI units for the constant a? Calculate: (a) the electric field E: (b) Vx E; Is Va possible electrostatic potential?; (c) the charge density p: (d) the energy density.
11. Consider the parabolic coordinate system (u, v) related to the Cartesian coordi- nates (r, y) by х — 2иv, y — u? — u? for (и, v) € [0, оо) х [0, оо) 1 u = 1, u 2' (a) Sketch in the ry-plane the curves given u = 2. Then sketch in 1 v = 1, v = 2. Shade in the region R the xy-plane the curves given v = 2' bounded by the curves given by...
Given the velocity potential for a 2-D incompressible flow, (x, y) = xy + x2 - y2 (a) Does the potential satisfy the Laplace Equation (i.e. V20 = 0)? What is the physical intepretation of this? (b) Find u(x,y) and v(x,y) (the corresponding velocity field of the flow). (c) Does the stream function y (x,y) exist? If so: (a) Find the stream function. (b) Find the implicit equation of streamline that passes through (x,y) = (1, 2).
6. You are in a region of space where the electric potential is given by: V(x,y,z) Voxy2ln(z) f for all points where z-0 (above the x-y plane)) Find an expression for the electric field Е(x, y, z). State this vectorially.
The electric potential depends on x and y as shown, for the
coordinate axes, in the figure (the potential does not depend on
z). The scale of the vertical axis is set by Vs = 500 V. What is
the direction of the electric field?
0.2 V (V) o'z od x(m) y (m)
(9 marks) QUESTION 4 a) Given vector field Éx,y,z) --yº coszi - 3xy cosz j+ xy" sinzk. Show that F is a conservative vector field. (4 marks) ii) Find the potential function, f such that F=Vf. (4 marks)
Given the potential V=x^yz2 [V] find the electric field E at (x 1,y=2,z=1 (i) (ii) calculate the work done in moving a 2 uC charge from A-(1,1,1) to B-(4,-1,1)
Please show work!!
(1 point) Take the system x' = 4x – xy, y = 5y + x2. How many critical points are there? What is the critical point with the largest x-coordinate? ( The linearization at this point is | tion at this point is [*] =A (Where A is where A is ul A = At this point the behavior is For behavior write one of "saddle", "source", "sink", "spiral sink", "spiral source", "center".
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