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Solve step by step, if you do not know do not answer, thanks 6. Rectangular pipe A rectangular metal pipe of length L w...
5. Consider a rectangular plate with one of the sides of length a lying along the...
5. Consider a rectangular plate with one of the sides of length a lying along the y axis and one of the sides of length b lying along the r axis. The interior of the plate is depleted of electric charge. Only the side lying along the line x = 0 is charged so that the electric potential on that side is held constant at Vo, for 0 < y <a, while the other sides of the plate are kept...
5) The figure below illustrates a large, flat, metal rectangular plate having large length, L (measured...
5) The figure below illustrates a large, flat, metal rectangular plate having large length, L (measured along the x-axis), large width, W (measured along the y-axis), and small thickness T (measured along the z-axis). Current I flows through the plate with uniform current density (directed along the positive x-axis) a) Use a symmetry argument to determine the direction of the magnetic field near the center of the plate at a field point, which is a distance z above the geometric...
Please solve using Gauss's Law of gravitation and explain it step by step 3) An infinite...
Please solve using Gauss's Law of gravitation and
explain it step by step
3) An infinite cylinder has radius a and is inite cylinder has radius a and is centered on the z axis. Along the length of this yinder, there is another cylinder with radius a and axis parallel to the z axis, passing through x=a/2, y=0. There is no mass outside the large cylinder. Inside the small cylinder, the mass density is Y3a (unit: kg/m?). Inside the large...
A rectangular loop of wire has a length 2a in the x direction and a width...
A rectangular loop of wire has a length 2a in the x direction and a width 2b in the y direction. The loop lies in the z = 0 plane and is centered at the origin. Assuming that the loop carries a current of I Amps counterclockwise, as viewed from the positive z axis, find the magnetic field vector H at the center of the loop. Hint: Consider how the contributions from opposite sides of the rectangle compare, to save...
1. Suppose that you place an uncharged, infinitely long metal cylinder of radius a in ain initial...
1. Suppose that you place an uncharged, infinitely long metal cylinder of radius a in ain initially uniform electric field EEo, such that the cylinder's axis lies along the z axis. The resulting electrostatic potential is V(x,y, z)V for points inside the cylinder, and Еда 2x V(x, y, z)-Й-Box + x2+3,2 for points outside the cylinder, where Vo is the (constant) electrostatic potential on the conductor. (a) Find the electric field, E, from the given voltage. (b) Find the charge...
5. Consider a long rectangular "gutter" of length a in the x direction and infi- nite...
5. Consider a long rectangular "gutter" of length a in the x direction and infi- nite height in the y direction. The gutter is infinitely long in the z direction, so the potential V inside the gutter only depends on x andy. The left (x-0,y), and right (r- a,y) sides of the gutter are grounded so that the potential V(x,y) is zero on those surfaces. The bottom surface of the gutter is kept fixed at a potential given by V(r,y-0)-...
A charged rod of length L lies along the z-axis, centered at the origin It has...
A charged rod of length L lies along the z-axis, centered at the origin It has a charge distribution: lambda(z) [\lambda_0 * z]/L a.) What coordinate system should be used to describe this system? Explain. b.) What is the total charge Q on the rod? c.) Find an equation for the electric field for (x, y, z), use any coordinate system d.)Find an algebraic equation for the electric field at z /2
An elliptical loop of axes of length a and b, centered at origin and lying in the y − z plane car...
An elliptical loop of axes of length a and b, centered
at origin and lying in the y − z plane carries current
I. The major axis of the ellipse is the ˆy.
1. What component of A is non-zero in the x − y plane?
[A qualitative argument will sufce]
2. Find an expression for B in terms of th non-zero components of
A.
3. What is the direction of B along i) the positive x axis and ii)...
Consider a cylinder of mass M, radius R and length L. (a) Calculate the inertia tensor...
Consider a cylinder of mass M, radius R and length L. (a) Calculate the inertia tensor for rotations about the center of mass in the frame where the z axis is along the axis of the cylinder. Use cylindrical coordinates, where x = r cos θ and y = r sin θ. (b) Find the inertia tensor in the frame where the center of the “bottom side” is at the origin with the z axis along the axis of the...
4.7. A rectangular waveguide (presented in Chapter 13) is a hollow conducting pipe oriented along the...
4.7. A rectangular waveguide (presented in Chapter 13) is a hollow conducting pipe oriented along the z axis, with an interior cross-section enclosed by conducting planes at x = 0 and a, and y = 0 and b (see Figure 13.7 for an illustration). The transverse electric mode field, TE1, defined for (0<x<a), (0 < y <b), is given by E, = Eožcos () sin (**)ą, – Ev sin (**) cos (*) ay where E, is a constant. a) Find...
5. Consider a rectangular plate with one of the sides of length a lying along the y axis and one of the sides of length b lying along the r axis. The interior of the plate is depleted of electric charge. Only the side lying along the line x = 0 is charged so that the electric potential on that side is held constant at Vo, for 0 < y <a, while the other sides of the plate are kept...
5) The figure below illustrates a large, flat, metal rectangular plate having large length, L (measured along the x-axis), large width, W (measured along the y-axis), and small thickness T (measured along the z-axis). Current I flows through the plate with uniform current density (directed along the positive x-axis) a) Use a symmetry argument to determine the direction of the magnetic field near the center of the plate at a field point, which is a distance z above the geometric...
Please solve using Gauss's Law of gravitation and
explain it step by step
3) An infinite cylinder has radius a and is inite cylinder has radius a and is centered on the z axis. Along the length of this yinder, there is another cylinder with radius a and axis parallel to the z axis, passing through x=a/2, y=0. There is no mass outside the large cylinder. Inside the small cylinder, the mass density is Y3a (unit: kg/m?). Inside the large...
1. Suppose that you place an uncharged, infinitely long metal cylinder of radius a in ain initially uniform electric field EEo, such that the cylinder's axis lies along the z axis. The resulting electrostatic potential is V(x,y, z)V for points inside the cylinder, and Еда 2x V(x, y, z)-Й-Box + x2+3,2 for points outside the cylinder, where Vo is the (constant) electrostatic potential on the conductor. (a) Find the electric field, E, from the given voltage. (b) Find the charge...
5. Consider a long rectangular "gutter" of length a in the x direction and infi- nite height in the y direction. The gutter is infinitely long in the z direction, so the potential V inside the gutter only depends on x andy. The left (x-0,y), and right (r- a,y) sides of the gutter are grounded so that the potential V(x,y) is zero on those surfaces. The bottom surface of the gutter is kept fixed at a potential given by V(r,y-0)-...
A charged rod of length L lies along the z-axis, centered at the origin It has a charge distribution: lambda(z) [\lambda_0 * z]/L a.) What coordinate system should be used to describe this system? Explain. b.) What is the total charge Q on the rod? c.) Find an equation for the electric field for (x, y, z), use any coordinate system d.)Find an algebraic equation for the electric field at z /2
An elliptical loop of axes of length a and b, centered
at origin and lying in the y − z plane carries current
I. The major axis of the ellipse is the ˆy.
1. What component of A is non-zero in the x − y plane?
[A qualitative argument will sufce]
2. Find an expression for B in terms of th non-zero components of
A.
3. What is the direction of B along i) the positive x axis and ii)...
4.7. A rectangular waveguide (presented in Chapter 13) is a hollow conducting pipe oriented along the z axis, with an interior cross-section enclosed by conducting planes at x = 0 and a, and y = 0 and b (see Figure 13.7 for an illustration). The transverse electric mode field, TE1, defined for (0<x<a), (0 < y <b), is given by E, = Eožcos () sin (**)ą, – Ev sin (**) cos (*) ay where E, is a constant. a) Find...
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