Ah arbnrary number nents, and all 2-companents separately to f of vector ately to find x-, y"r z-...
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addition, show the unit vectors r, θ, and φ at that point B. Write the vectors ŕ.0, and ф in terms of the unit vectors x, y, and г. Here's the easy way to do this 1. For r, simply use the fact that/r 2. For φ, use the following formula sin θ Explain why the above formula works 3. Compute θ via θ...
2. A thin ring of radius R in the x - y plane is centered at the coordinate origin, and is charged with linear charge density λ which depends* on the polar angle θ as (9) λο sin(0), where 0 > 0, and θ . (a) Plot λ(0) for θ [0.2n]. (b) Before doing any calculations, sketch the electric field vector vector at the coor- - 0 is on the positive r-axis dinate origin in the direction you expect it...
1. Sketch the vector field F x, y+(y-x)j F(x, y x, y f 2. Find the gradient vector field of f(r, y)-xe" 1. Sketch the vector field F x, y+(y-x)j F(x, y x, y f 2. Find the gradient vector field of f(r, y)-xe"
2dddd0100bb/8216135?response- * LA89 VECTORS (PART 2) R 1Ri1=4 2) Keep in mind that Ř, and Ra can be represented by 60 fix Ano TR1=4 60 X To their respective andy Components. Hence, if we add x, and a we will have На хотелот 2 к. 4 г. andef whold of, and I, care will have the y component of R1+R2. 3) add all & components and all IR, I means the magnitude o R We will now add R and...
PPLEASE SOLVE NUMBER 6 ONLY Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) x' =-x + 2y r(0) 2, y(0)1 r(0) 0, y(0)-2 Determine the nullclines, sketch the vector field, and then solve the problem. (All derivatives are with respect to t.) x' =-x + 2y r(0) 2, y(0)1 r(0) 0, y(0)-2