EX : a) determine wheter F is Conservative and find a potential if it is.. b) Find the work done by F(x₁y/2) = (y² cosx + 2² ) + ²+ 2y sinx). z) a particle + 3x2² K² in moving the planes X+Y-2t =0 From (π/2, ½/₂, T/₂2) to (37/₂2, 35/2, 37/2). a long the intersection of and x-2y + 2 =0

Consider a particle of mass m acted upon by a central potential (r is distance and a>0 is a constant): U (r) p2 a) What are the constants of the motion? b) Is a circular orbit possible in this potential? If so, state the conditions for it. c) Under what conditions will the particle fall to the center of the potential (r = 0)?

Two large charged plates of charge density ±18µC/m² face each other at a separation of 7 mm. Choose coordinate axes so that both plates are parallel to the xy plane, with the negatively charged plate located at z = 0 and the positively charged plate at z = +7 mm. Define potential so that potential at z = 0 is zero (V(z = 0) = 0). Hint a. Find the electric potential at following values of z: o potential at z = -7 mm: V(z = -7 mm) = o potential at z = +1 mm: V(z = +1 mm): = o potential at z = +7 mm: V(z = +7 mm) = = o potential at z = +9.2 mm: V(z = +9.2 mm) = V. V. V. V. b. An electron is released from rest at the negative plate. With what speed will it strike the positive plate? The electron will strike the positive plate with speed of m/s. (Use "E" notation to enter your answer in scientific notation. For example, to enter 3.14 × 10¹2, enter "3.14E12".)

The question is appended to the image:

Please solve asap: 7. Find a potential function, and you don’t need to verify that they are conservative because they are (a) F = < -y , x > (b) F = < yz, xz, xy >

In free space, the retarded potentials are given by V = x(z - ct)V, 1 √μE (a) Prove that V. A = μ& (b) Determine E. where c = av at A = x(z/c- t)a₂ Wb/m