A charged particle moving in a magnetic field will experience a magnetic force. Suppose that the magnetic force experienced by the moving charged particle can be described by the vector field F(x, y) (a) Evaluate F(0,1), F(1,0), F(0,2). F(2,0), F(1,1), F(2,2), F(1,2), F(2,1). (b) Describe F by sketching the vectors from Question 6(a) in the first quadrant plane.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 32E
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Needed to be solved a and b part correctly in one hour please show neat and clean work
Question 6
A charged particle moving in a magnetic field will experience a magnetic force. Suppose that
the magnetic force experienced by the moving charged particle can be described by the vector
field
F(x, y) =
(a)
Evaluate F(0,1), F(1,0), F(0,2), F(2,0), F(1,1), F(2,2), F(1,2), F(2,1).
(b)
Describe F by sketching the vectors from Question 6(a) in the first quadrant plane.
(c)
Determine if F is a conservative vector field.
Given that the charged particle is moving along the straight line from (3, – 3) to (0,3),
as represented by the solid line in the figure below.
(d)
l(0, 3)
(0, 0)
X,
(3, -3)
Figure Q6(d)
Calculate the work done by the magnetic force given by the integral
F. dr,
where C is the straight line from (3, –3) to (0,3).
Now, consider the polygonal region with vertices (0, 3), (0,0) and (3, – 3) as shown
in the figure above (the region bounded by the dotted and solid lines), use Green's
Theorem to calculate the work done
(e)
.dr
where C is the straight line described in Question 6(d).
Transcribed Image Text:Question 6 A charged particle moving in a magnetic field will experience a magnetic force. Suppose that the magnetic force experienced by the moving charged particle can be described by the vector field F(x, y) = (a) Evaluate F(0,1), F(1,0), F(0,2), F(2,0), F(1,1), F(2,2), F(1,2), F(2,1). (b) Describe F by sketching the vectors from Question 6(a) in the first quadrant plane. (c) Determine if F is a conservative vector field. Given that the charged particle is moving along the straight line from (3, – 3) to (0,3), as represented by the solid line in the figure below. (d) l(0, 3) (0, 0) X, (3, -3) Figure Q6(d) Calculate the work done by the magnetic force given by the integral F. dr, where C is the straight line from (3, –3) to (0,3). Now, consider the polygonal region with vertices (0, 3), (0,0) and (3, – 3) as shown in the figure above (the region bounded by the dotted and solid lines), use Green's Theorem to calculate the work done (e) .dr where C is the straight line described in Question 6(d).
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