Question

Calculate the work done by the field F⃗ = (x 3 + z 2 , ey + x 2 , z8 + y 2 ) when a particle moves under its influence around the edge of the part of the sphere x 2 + y 2 + z 2 = 1 lying in the octant x >= 0, y <= 0, z <= 0, in the counterclockwise direction as seen from above. counterclockwise as seen from above

Name: calculate the work done by the field f x 3 z 2 ey x 2 z8 y 2 when a particle moves under its influence around the edge of the part of the sphere x 2 y 2 z 2 1 lying in the octant x 0 y 0 z 0 69615
Uploaded: 2023-08-15T16:59:44-08:00
Duration: 3 min 3 s
Channel: Madhur L
Description: calculate the work done by the field f x 3 z 2 ey x 2 z8 y 2 when a particle moves under its influence around the edge of the part of the sphere x 2 y 2 z 2 1 lying in the octant x 0 y 0 z 0 69615

          Calculate the work done by the field F⃗ = (x 3 + z 2 , ey + x 2 , z8 + y 2 ) when a particle moves under its influence around the edge of the part of the sphere x 2 + y 2 + z 2 = 1 lying in the octant x >= 0, y <= 0, z <= 0, in the counterclockwise direction as seen from above.
counterclockwise as seen from above

Added by Kathy C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

08/15/2023

Step 1

We can use spherical coordinates to do this. Let's use the parameterization: x = cos(t) y = -sin(t) z = 0 where t ranges from 0 to π/2 to cover the octant. Show more…

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Calculate the work done by the field F⃗ = (x 3 + z 2 , ey + x 2 , z8 + y 2 ) when a particle moves under its influence around the edge of the part of the sphere x 2 + y 2 + z 2 = 1 lying in the octant x >= 0, y <= 0, z <= 0, in the counterclockwise direction as seen from above. counterclockwise as seen from above