2. Find the work done by the force field F(x, y) = yi + xy j of a particle moves from (1, 0) to (-1, 0) along the circle x² + y² = 9.

Find the outward flux of F = (4x + 25y²,0. 10z through the surface 3 = 1. 25 4

A Particle moves way 2 x² + y² = 4 oriented in the half dove on around the circle counter-clockwise direction starting at (2.0). find the work the Particle with the force field f = (x² + 2xy>

B = ①check that div (B) = 0 ②Find a vector potential for B.

A force field is given by the equation. A particle is moved from (1,0,0) to (1,1,1) along a straight line. Calculate the work done by the force field on the particle.

Let (4xy-3x²z²)₁ + (2x²)Ĵ − 2x³ zk = (i) Find a scalar potential for F. (x, y, z) = - note: Answer should have "+C" in it, where C is some constant (ii) Find the work done in moving from (1,1,0) to (2, −1, 1) by the above force field. W= (iii) Solve the differential equation (4xy - 3x²²)dx + 2x²dy - 2x³zdz = 0 ☐ = K, where K is a constant

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from (2,0) to (-2,0)

Find the work done by a force F = 6ỉ + 57– 3k when a particle moves from point | P(-3, 4, 5) to point Q(2, -3, -1) in space.

Find the work So F. dr done by the force field F = (y, x, z) on a particle that moves along C the line segment from (1, -3, 2) to (4, 6,-5).