Prove that If two geodesics r and r' are parallel transports along another geodesic l, then they are also parallel transports along any geodesic passing through the midpoint of the segment of l between r and r'.
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Prove that If two geodesics r and r' are parallel transports
along another geodesic l, then...
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle betwe...
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle between v and w. (b) Consider the projection proj, w of w onto v, and then project this projection on u to get proju (proj, w). Is this necessarily equal to the projection proj, w of w on u? Prove or give a counterexample. (c) Find the volume of the parallelepiped with edges formed by u-(2,5,c), v (1,1,1) and w...
7. (10) Find the flaw in the following attempted proof of the parallel postulate by Wolfgang Bolyai (Hungarian, 1775 - 1856) (see Fig. 3). Given any point P not on a line l, construct a line 1&#...
7. (10) Find the flaw in the following attempted proof of the parallel postulate by Wolfgang Bolyai (Hungarian, 1775 - 1856) (see Fig. 3). Given any point P not on a line l, construct a line 1' parallel to through P in the usual way: drop a perpendicular PQ to / and construct /" perpendicular to PQ. Let I" be any line through P distinct from l'. To see that /" intersects I, pick a point A on PQ between...
Consider the situation shown below in which you have two plates of radius R = 1.25 cm which have ...
Consider the situation shown below in which you have two plates of radius R = 1.25 cm which have between them an electric field given by一4t V/m. The electric field is 0 everywhere except between those plates. You are interested in calculating the magnetic field a distance r 9.5 cm away from the midpoint between the plates We'll walk through the various pieces of Ampere's Law through the course of the problem. a. What is the enclosed current within the...
10. [-/1 Points] DETAILS SERPSE10 36.2.OP.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER (a) A riverside...
10. [-/1 Points] DETAILS SERPSE10 36.2.OP.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER (a) A riverside warehouse has several small doors facing the river. Two of these doors are open as shown in the figure below. Closed door B Open door Open door L The walls of the warehouse are lined with sound-absorbing material. Two people stand at a distance L - 100 m from the wall with the open doors. Person A stands along a line passing through the...
using these axioms prove proof number 5 1 - . Axiom 1: There exist at least...
using these axioms prove proof number 5
1 - . Axiom 1: There exist at least one point and at least one line Axiom 2: Given any two distinct points, there is exactly one line incident with both points Axiom 3: Not all points are on the same line. Axiom 4: Given a line and a point not on/ there exists exactly one linem containing Pouch that / is parallel tom Theorem 1: If two distinct lines are not parallet,...
Results given on page 300 TABLE 12.2 Moments of inertia of objects with uniform density Object...
Results given on page 300 TABLE 12.2 Moments of inertia of objects with uniform density Object and axis Picture Object and axis Picture Thin rod, about center | Cylinder or disk, about center MR ML2 Thin rod, about end ML Cylindrical hoop. MR2 about center | Solid sphere, about diameter Маг Plane or slab, about center Ma2 MR Plane or slab, about edge Ma2 Spherical shell, about diameter MR2 1. b. A very thin, straight, uniform rod has a length...
Two identical small current carrying loops of wire are oriented along a common axis with the...
Two identical small current carrying loops of wire are oriented along a common axis with the plane of their loops parallel to each other. See Figure EC. The distance between the loops, x, is much larger than the radius of each loop, R. The magnetic dipole moment of each loop is directed parallel to the axis, and the magnetic field that one loop creates at the center of the other loop is also parallel to the axis. So mu^rightarrow and...
1. Two parallel wires separated by a distance l 1.0m are carrying currents l1- 15A and...
1. Two parallel wires separated by a distance l 1.0m are carrying currents l1- 15A and I2 7A in the direction shown in tHe diagram. Halfway between the two wires is a small solenoid, consisting of N- 8 loops with radius r. a) Assume the solenoid is small enough that the magnetic field in the vicinity of the solenoid is uniform and equal to the value at the centre of the solenoid. If the magnetic flux through the solenoid is...
i want answers of all Questions Example. As another special case of examples we may regard...
i want answers of all Questions
Example. As another special case of examples we may regard the set R of all of n umber vector 1.4.6. Example. Yet another al l the vector space M of mx matrices of members of where m - NI. We will use M. horthand for M F ) and M. for M.(R) 1.4.9. Exercise. Let be the total real numbers. Define an operation of addition by y the maximum of u and y for...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle between v and w. (b) Consider the projection proj, w of w onto v, and then project this projection on u to get proju (proj, w). Is this necessarily equal to the projection proj, w of w on u? Prove or give a counterexample. (c) Find the volume of the parallelepiped with edges formed by u-(2,5,c), v (1,1,1) and w...
7. (10) Find the flaw in the following attempted proof of the parallel postulate by Wolfgang Bolyai (Hungarian, 1775 - 1856) (see Fig. 3). Given any point P not on a line l, construct a line 1' parallel to through P in the usual way: drop a perpendicular PQ to / and construct /" perpendicular to PQ. Let I" be any line through P distinct from l'. To see that /" intersects I, pick a point A on PQ between...
Consider the situation shown below in which you have two plates of radius R = 1.25 cm which have between them an electric field given by一4t V/m. The electric field is 0 everywhere except between those plates. You are interested in calculating the magnetic field a distance r 9.5 cm away from the midpoint between the plates We'll walk through the various pieces of Ampere's Law through the course of the problem. a. What is the enclosed current within the...
10. [-/1 Points] DETAILS SERPSE10 36.2.OP.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER (a) A riverside warehouse has several small doors facing the river. Two of these doors are open as shown in the figure below. Closed door B Open door Open door L The walls of the warehouse are lined with sound-absorbing material. Two people stand at a distance L - 100 m from the wall with the open doors. Person A stands along a line passing through the...
using these axioms prove proof number 5
1 - . Axiom 1: There exist at least one point and at least one line Axiom 2: Given any two distinct points, there is exactly one line incident with both points Axiom 3: Not all points are on the same line. Axiom 4: Given a line and a point not on/ there exists exactly one linem containing Pouch that / is parallel tom Theorem 1: If two distinct lines are not parallet,...
Results given on page 300 TABLE 12.2 Moments of inertia of objects with uniform density Object and axis Picture Object and axis Picture Thin rod, about center | Cylinder or disk, about center MR ML2 Thin rod, about end ML Cylindrical hoop. MR2 about center | Solid sphere, about diameter Маг Plane or slab, about center Ma2 MR Plane or slab, about edge Ma2 Spherical shell, about diameter MR2 1. b. A very thin, straight, uniform rod has a length...
Two identical small current carrying loops of wire are oriented along a common axis with the plane of their loops parallel to each other. See Figure EC. The distance between the loops, x, is much larger than the radius of each loop, R. The magnetic dipole moment of each loop is directed parallel to the axis, and the magnetic field that one loop creates at the center of the other loop is also parallel to the axis. So mu^rightarrow and...
1. Two parallel wires separated by a distance l 1.0m are carrying currents l1- 15A and I2 7A in the direction shown in tHe diagram. Halfway between the two wires is a small solenoid, consisting of N- 8 loops with radius r. a) Assume the solenoid is small enough that the magnetic field in the vicinity of the solenoid is uniform and equal to the value at the centre of the solenoid. If the magnetic flux through the solenoid is...
i want answers of all Questions
Example. As another special case of examples we may regard the set R of all of n umber vector 1.4.6. Example. Yet another al l the vector space M of mx matrices of members of where m - NI. We will use M. horthand for M F ) and M. for M.(R) 1.4.9. Exercise. Let be the total real numbers. Define an operation of addition by y the maximum of u and y for...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...
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