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a) Show that in cylindrical coordinates (r, ø z) the Christoffel symbols I2 and r2 are...
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by y = p sin d, p cos integer, find expressions...
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by y = p sin d, p cos integer, find expressions for the following quantities in where p 0,0 < 0 < 2t. If n is an terms of p, ф, z and p, ф, 2. (а) Vф; (b) Vр"3; (c) V2(p2 cos ); (d) V :(pp + pфф + z2); (F) V. (p*-1 sin(nф)р + pr-1 cos(nф)ф). (e) V x
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by...
In cylindrical coordinates (r, , z), a torus (a.k.a. the mathematical doughnut) has the equation Change the coordinate...
In cylindrical coordinates (r, , z), a torus (a.k.a. the mathematical doughnut) has the equation Change the coordinate system from cylindrical coordinates (r, , z) to torodial coordinates () where Find the surface area of the torus. We were unable to transcribe this imager-a We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image r-a
You are given the metric of a 4-dimensional Einstein universe in terms of spherical polar coordinates r, 0, ø, -dt2e20(...
You are given the metric of a 4-dimensional Einstein universe in terms of spherical polar coordinates r, 0, ø, -dt2e20(1) dr2 +r2 (d02 + sin2 0dp2), ds2 (a) Use the variational principle 2 ds dA 0, dA to find the geodesic equation for r with parameter A, between given points X1 and A2. (b) Deduce or otherwise show that Г — Ф", Ге — —re 20, To= -rsin2 Oe-24 rr =0 if uv and T T
You are given the...
1.18. Points P and P' have spherical coordinates (r,0,y) and (r,θ,φ), cylindrical coordinates (p, p, z)...
1.18. Points P and P' have spherical coordinates (r,0,y) and (r,θ,φ), cylindrical coordinates (p, p, z) and (p',p',z'), and Cartesian coordinates (x, y, z) and (x',y',z'), respectively. Write r - r in all three coordinate systems. Hint: Use Equation 1.2) with a r r and r and r' written in terms of appropriate unit vectors.
2014/B5 (a) Draw skecthes to illustrate R, 0 and z coordinate curves for the case of cylindrical polar coordinates (b) Show that the gradient of a scalar field, p, can be expressed in terms of cu...
2014/B5 (a) Draw skecthes to illustrate R, 0 and z coordinate curves for the case of cylindrical polar coordinates (b) Show that the gradient of a scalar field, p, can be expressed in terms of curvilinear coordinates u1, u2 and us, of an orthogonal coordinate system as where h, Idr/dul. Hence obtain a formula for Vip in cylindrical polar coordinates. (c) Evaluate dp/ds, the rate of change of φ with distance, for the field φ-R, cost) at the point R...
N Question (Char3) LL** The integral 9-423 xz dzdydx in cylindrical coordinates is (A) SL, $°r?...
N Question (Char3) LL** The integral 9-423 xz dzdydx in cylindrical coordinates is (A) SL, $°r? cos @ z dzdrde (B) 12" ! r2 cos @ z dzdrde C) $*$$* r2 cos z dzdrde (D) $*$$*r cos 8 z dzdrde (E) ST 8r2 cose z dzdrde (A) O (B) O (C) O (D) O
Dynamic 4. Compare rectangular coordinates with polar coordinates and cylindrical coordinates. Rectangular Cylindr...
Dynamic
4. Compare rectangular coordinates with polar coordinates and cylindrical coordinates. Rectangular Cylindrical Polar X, Y. Z R 5. For a circular motion, what are the normal and tangential components of the acceleration in the polar coordinates. Normal component ? Tangential component ? m
4. Compare rectangular coordinates with polar coordinates and cylindrical coordinates. Rectangular Cylindrical Polar X, Y. Z R 5. For a circular motion, what are the normal and tangential components of the acceleration in the polar coordinates....
Particle in a cylindrically symmetrical potential Let p, o, z be the cylindrical coordinates of a...
Particle in a cylindrically symmetrical potential Let p, o, z be the cylindrical coordinates of a spinless 1. (x = ? coso, y = ? sin ?, p 0, 0 <p < 2?). Assume that the potential en of this particle depends only on , and not on ? and z. Recall that: a. Write, in c ylindrical coordinates, the differential operator associated with the Hamiltonian. Show that H commutes with L, and P. Show fr the wave functions chosen...
4. (12 points) Ampere's law in cylindrical coordinates (p,p,z.) An infinitely long coaxial cable is given in the fi...
4. (12 points) Ampere's law in cylindrical coordinates (p,p,z.) An infinitely long coaxial cable is given in the figure below. The inner conductor has a radius of R1 = 1.00cm. The outer conductor has a radius R2 = 2.00cm and has negligible thickness. The inner conductor has a current density given by J 2.00A p (TR1) flowing out of the page (positive z direction), where ρ is the radial direction. The outer conductor has a current 1 of 1.00 Amperes...
Write the vector differential operator "DEL-V in Cartesian coordinates Cylindrical coordinates Spherical coordinates. 2. Show for...
Write the vector differential operator "DEL-V in Cartesian coordinates Cylindrical coordinates Spherical coordinates. 2. Show for any "nice" scalar function (x,y,z), the Curl of the gradient of (x,y,z) is Zero.. VxVo = 0 Hint: assume the order of differentiation can be switched 3. Find the volume of a sphere of radius R by integrating the infinitesimal volume element of the sphere. 4. Write Maxwell's equations for the case of electro and magneto statics (the fields do not change in time)...
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by y = p sin d, p cos integer, find expressions for the following quantities in where p 0,0 < 0 < 2t. If n is an terms of p, ф, z and p, ф, 2. (а) Vф; (b) Vр"3; (c) V2(p2 cos ); (d) V :(pp + pфф + z2); (F) V. (p*-1 sin(nф)р + pr-1 cos(nф)ф). (e) V x
106. Cylindrical Coordinates. Define curvilinear coordinates (p, ø, z) by...
You are given the metric of a 4-dimensional Einstein universe in terms of spherical polar coordinates r, 0, ø, -dt2e20(1) dr2 +r2 (d02 + sin2 0dp2), ds2 (a) Use the variational principle 2 ds dA 0, dA to find the geodesic equation for r with parameter A, between given points X1 and A2. (b) Deduce or otherwise show that Г — Ф", Ге — —re 20, To= -rsin2 Oe-24 rr =0 if uv and T T
You are given the...
1.18. Points P and P' have spherical coordinates (r,0,y) and (r,θ,φ), cylindrical coordinates (p, p, z) and (p',p',z'), and Cartesian coordinates (x, y, z) and (x',y',z'), respectively. Write r - r in all three coordinate systems. Hint: Use Equation 1.2) with a r r and r and r' written in terms of appropriate unit vectors.
2014/B5 (a) Draw skecthes to illustrate R, 0 and z coordinate curves for the case of cylindrical polar coordinates (b) Show that the gradient of a scalar field, p, can be expressed in terms of curvilinear coordinates u1, u2 and us, of an orthogonal coordinate system as where h, Idr/dul. Hence obtain a formula for Vip in cylindrical polar coordinates. (c) Evaluate dp/ds, the rate of change of φ with distance, for the field φ-R, cost) at the point R...
N Question (Char3) LL** The integral 9-423 xz dzdydx in cylindrical coordinates is (A) SL, $°r? cos @ z dzdrde (B) 12" ! r2 cos @ z dzdrde C) $*$$* r2 cos z dzdrde (D) $*$$*r cos 8 z dzdrde (E) ST 8r2 cose z dzdrde (A) O (B) O (C) O (D) O
Dynamic
4. Compare rectangular coordinates with polar coordinates and cylindrical coordinates. Rectangular Cylindrical Polar X, Y. Z R 5. For a circular motion, what are the normal and tangential components of the acceleration in the polar coordinates. Normal component ? Tangential component ? m
4. Compare rectangular coordinates with polar coordinates and cylindrical coordinates. Rectangular Cylindrical Polar X, Y. Z R 5. For a circular motion, what are the normal and tangential components of the acceleration in the polar coordinates....
Particle in a cylindrically symmetrical potential Let p, o, z be the cylindrical coordinates of a spinless 1. (x = ? coso, y = ? sin ?, p 0, 0 <p < 2?). Assume that the potential en of this particle depends only on , and not on ? and z. Recall that: a. Write, in c ylindrical coordinates, the differential operator associated with the Hamiltonian. Show that H commutes with L, and P. Show fr the wave functions chosen...
4. (12 points) Ampere's law in cylindrical coordinates (p,p,z.) An infinitely long coaxial cable is given in the figure below. The inner conductor has a radius of R1 = 1.00cm. The outer conductor has a radius R2 = 2.00cm and has negligible thickness. The inner conductor has a current density given by J 2.00A p (TR1) flowing out of the page (positive z direction), where ρ is the radial direction. The outer conductor has a current 1 of 1.00 Amperes...
Write the vector differential operator "DEL-V in Cartesian coordinates Cylindrical coordinates Spherical coordinates. 2. Show for any "nice" scalar function (x,y,z), the Curl of the gradient of (x,y,z) is Zero.. VxVo = 0 Hint: assume the order of differentiation can be switched 3. Find the volume of a sphere of radius R by integrating the infinitesimal volume element of the sphere. 4. Write Maxwell's equations for the case of electro and magneto statics (the fields do not change in time)...
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