1. ### Calculating crossproduct integral, Parametrization

i) I approximate the solenoid as a cylinder with height L and radius R. I am not sure how I am supposed to place the solenoid in the coordinate system but I think it must be like this, right? The surface occupied by the cylinder can be described by all vectors ##\vec x =(x,y,z)## so that...
2. ### How to get the magnetic moment for this loop?

About this figure, the current in the opposite wires are parallel (and not anti-parallel). So, for instance for the first option the torque is zero; but I wanted to know what is the magnetic moment of this loop. Since I rely only on formula I've have no idea how to compute for this one.
3. ### Lie Bracket and Cross-Product

Prove that for a 2 sphere in R3 the Lie bracket is the same as the cross product using the vector: X = (y,-x,0); Y = (0,z-y) [X,Y] = JYX - JXY where the J's are the Jacobean matrices. I computed JYX - JXY to get (-z,0,x). I computed (y,-x,0) ^ (0,z,-y) and obtained (xy,y2,yz) = (z,0,x)...
4. ### Vector Cross Product With Its Curl

Starting with LHS: êi εijk Aj (∇xA)k êi εijk εlmk Aj (d/dxl) Am (δil δjm - δim δjl) Aj (d/dxl) Am êi δil δjm Aj (d/dxl) Am êi - δim δjl Aj (d/dxl) Am êi Aj (d/dxi) Aj êi - Aj (d/dxj) Ai êi At this point, the LHS should equal the RHS in the problem statement, but I have no clue where...
5. ### Stuck on a few Vector homework problems

I'm stuck on a few Vector homework problems. I don't quite understand how to write vectors A+B and A-B for questions 1b and 2b. I tried starting with calculating the magnitude for vector A+B on question 1b and then followed by finding theta, but I'm not sure if that's what I'm supposed to do...
6. ### I Understanding the cross product and rotations

Hi I have used cross products thousands of time without really knowing what it actually does; I know how to compute it, but I don't feel like I understand it. Also, when it shows up in physics/kinematics contexts, it's only because the magnitudes of the vectors involved have to be multiplied...
7. ### Vectors and vector addition

Homework Statement Calculate |u+v+w|, knowing that u, v, and w are vectors in space such that |u|=√2, |v|=√3, u is perpendicular to v, w=u×v. Homework Equations |w|=|u×v|=|u|*|v|*sinΘ The Attempt at a Solution [/B] Θ=90° |w|=(√2)*(√3)*sin(90°)=√(6) Then I tried to use u={√2,0,0}...
8. ### B How to specify the direction of an area vector?

We all know that the area of a triangle having consecutive sides as ##\vec { a }## and ##\vec { b }## has the area ##\frac { 1 } { 2 } | \vec { a } \times \vec { b } |## but what is the direction of that area vector? I mean if we consider ##\vec { a } \times \vec { b }## that will be one...
9. ### Angular momentum relative to the origin

Homework Statement A 2.4 kg particle-like object moves in a plane with velocity components vx = 25 m/s and vy = 80 m/s as it passes through the point with (x, y)coordinates of (3.0, −4.0) m. (Express your answers in vector form.) (a) What is its angular momentum relative to the origin at this...

18. ### B Torque and forces parallel vs perpendicular to the axis of rotation...

why force parallel to the axis of rotation do not make any torque.
19. ### I Is there a true upward force on a rotating object?

I understand that the torque on a gyrating object is defined as the force vector cross multiplied by the lever arm position vector, which produces a resultant vector that is normal to both of the original vectors. However, when an object (let's say a disk) is rotating about an axis...
20. ### Calculating magnetic force on semicircle conductor

Homework Statement Given the figure below[/B] I need to calculate the total magnetic force on the semicircle section of the conductor. Current is I, Radius is R, and the Magnetic Field is B. Homework Equations d\vec{F} = Id\vec{l} \times \vec{B}[/B] The Attempt at a Solution [/B] dl is...
21. ### Proof involving central acceleration and vector products

Homework Statement Suppose r:R\rightarrow { V }_{ 3 } is a twice-differentiable curve with central acceleration, that is, \ddot { r } is parallel with r. a. Prove N=r\times \dot { r } is constant b. Assuming N\neq 0, prove that r lies in the plane through the origin with normal N. Homework...
22. ### Prove area of triangle is given by cross products of the vertex vectors...

Homework Statement The three vectors A, B, and C point from the origin O to the three corners of a triangle. Show that the area of the triangle is given by 1/2|(BxC)+(CxA)+(AxB)|. Homework Equations The Attempt at a Solution I know that the magnitude of the cross product of any two vectors...
23. ### Cross Product Properties Question

Homework Statement A\cdot B\times C\quad =\quad 2\\ (2A+B)\quad \cdot \quad [(A-C)\quad \times \quad (2B+C)]\quad =\quad ? Homework Equations Various cross product and dot product properties The Attempt at a Solution I've only managed to get so far, don't really know what to do next A\cdot...
24. ### B Deriving law of sines from cross product

I am trying to derive the law of signs from the cross product. First, we have three vectors ##\vec{A} ~\vec{B} ~\vec{C}## such that ##\vec{A} + \vec{B} + \vec{C} = 0##. This creates a triangle. Then, we label the angles opposite the respective sides as a, b, and c. I am not sure where to go...
25. ### A Hodge Dual as Sequence of Grade Reducing Steps

If we seek a bijection $$\wedge^p V \to \wedge^{n-p} V$$ for some inner product space ##V##, we might think of starting with the unit ##n##-vector and removing dimensions associated with the original vector in ##\wedge^p V ##. Might this be expressed as a sequence of steps by some binary...
26. ### A Exterior Algebra Dual

The determinant of some rank 2 tensor can be expressed via the exterior product. $$T = \sum \mathbf{v}_i \otimes \mathbf{e}_i \;\;\; \text{or}\sum \mathbf{v}_i \otimes \mathbf{e}^T_i$$ $$\mathbf{v}_1\wedge \dots \wedge \mathbf{v}_N = det(T) \;\mathbf{e}_1\wedge \dots \wedge\mathbf{e}_N$$ The...
27. ### Understanding solution method for finding accelerations in a mechanical linkage

Homework Statement I was checking my work and Chegg uses the equations differently. Can somebody tell me why? Maybe I'm misunderstanding how/why to use the equation I chose. Homework Equations They say aB = -ω2ABRB/Ai I used aB = aA + αk x r - ω2rB/A The Attempt at a Solution So...
28. ### Understanding cross product and direction of torque

Homework Statement Hi everyone, I am a first year physics student and we recently learned about torque. Every time I think I understand it something else comes up to confuse me - this time it is the direction. I tried looking in the forum and generally in google, but everyone only explains the...
29. ### Confusion about how to identify lever arm

Homework Statement A rotational axis is directed perpendicular to the plane of a square and is located as shown in the drawing. Two forces, F1 and F2, are applied to diagonally opposite corners, and act along the sides of the square, first as shown in part a and then as shown in part b of the...
30. ### Layman explanation of some simple EM equations

So its been a while since I studied maxwells equations, anyway: So From my ignorant perspective, trying to derive conceptual meaning from these, I can see that the time dependant study there is some conductivity x the partial differential of the magnetic vector potential plus the cross product...