Question

Problem 1: Given \(\vec{B} = 8x\hat{a}_y - 2y\hat{a}_x\) 1. Do the integral \(\oint \vec{B} \cdot d\vec{l}\) for the path that enclosed the following surface \(z = 0, 1 \ge x \ge 3, 2 \ge y \ge 5\) going from \((x = 0, y =10)\) in CCW through the square. 2. Find the curl of B 3. Evaluate the curl of B over the surface that is defined in part a 4. Compare your results of part 1 and 3? What do you see? Explain/ discuss (not a short answer, please talk abou tit. Problem 2: You are given the following vectors in spherical system \(\vec{A} = \frac{Kr}{10}\hat{r}\) in \(\frac{C}{m^2}\) where K is a constant with a unit. a. What is the unit of K? b. Set up and evaluate. \(\oint \vec{A} \cdot d\vec{s}\) (the net flux of A though the closed surface) of a sphere with r=2m centered at the origin. c. Find \(\iiint_V \nabla \cdot \vec{A} \, dv\) for the volume of sphere of radius 4. Need to clearly define and identify the direction of your closed path

          Problem 1: Given \(\vec{B} = 8x\hat{a}_y - 2y\hat{a}_x\)
1. Do the integral \(\oint \vec{B} \cdot d\vec{l}\) for the path that enclosed the following surface
\(z = 0, 1 \ge x \ge 3, 2 \ge y \ge 5\) going from \((x = 0, y =10)\)
in CCW through the square.
2. Find the curl of B
3. Evaluate the curl of B over the surface that is defined in part a
4. Compare your results of part 1 and 3? What do you see? Explain/
discuss (not a short answer, please talk abou tit.
Problem 2: You are given the following vectors in spherical system \(\vec{A} = \frac{Kr}{10}\hat{r}\) in \(\frac{C}{m^2}\)
where K is a constant with a unit.
a. What is the unit of K?
b. Set up and evaluate. \(\oint \vec{A} \cdot d\vec{s}\) (the net flux of A though the closed
surface) of a sphere with r=2m centered at the origin.
c. Find \(\iiint_V \nabla \cdot \vec{A} \, dv\) for the volume of sphere of radius 4.
Need to clearly define and identify the
direction of your closed path

Problem 1: Given B⃗ = 8xây - 2yâx
1. Do the integral ∮B⃗· dl⃗ for the path that enclosed the following surface
z = 0, 1 ≥ x ≥ 3, 2 ≥ y ≥ 5 going from (x = 0, y =10)
in CCW through the square.
2. Find the curl of B
3. Evaluate the curl of B over the surface that is defined in part a
4. Compare your results of part 1 and 3? What do you see? Explain/
discuss (not a short answer, please talk abou tit.
Problem 2: You are given the following vectors in spherical system A⃗ = (Kr)/(10)r̂ in (C)/(m^2)
where K is a constant with a unit.
a. What is the unit of K?
b. Set up and evaluate. ∮A⃗· ds⃗ (the net flux of A though the closed
surface) of a sphere with r=2m centered at the origin.
c. Find ∇·A⃗ dv for the volume of sphere of radius 4.
Need to clearly define and identify the
direction of your closed path

Added by Jessica Z.

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