There are two stationary fields of force F=ayiand F=axi+byj, where i and j are the unit vectors of the x and y axes, and a and b are constants. Find out whether these fields are potential.

A particle moves in the plane xy with velocity v=ai+bxj , where i and j are the unit vectors of the x and y axes, and a and b are constants. At the initial moment of time the particle was located at the point x=y=0 . Find: (a) the equation of the particle's trajectory y(x) , (b) the curvature radius of trajectory as a function of x.

A force F_1=Aj is applied to a point whose radius vector r_1=ai , while a force F_2=Bi is applied to the point whose radius vector r_2=bj . Both radius vectors are determined relative to the origin of coordinates O, i and j are the unit vectors of the x and y axes, a, b, A, B are constants. Find the arm l of the resultant force relative to the point O.

A force F=Ai+Bj is applied to a point whose radius vector relative to the origin of coordinates O is equal to r=ai+bj , where a, b, A, B are constants, and i,j are the unit vectors of the x and y axes. Find the moment N and the arm l of the force F relative to the point O.

In an interial reference frame K there is only magnetic field with induction B = b (yl -x)//(x^(2) + y^(2)) , where b is a constane, i and j are the unit vectors of the x and y axes. Find the elecric field strength E' in the frame K' moving relative to the frame K with a constatn non-relative velocity v = vk, k is the unit vector of the z-axis. The z' axis is assumed to coincule with the z axis. What is the shape of the field E' ?

The electric field strength depends only on the x and y coordinates according to the law E = a (x i + yj) (x^(2) + y^(2)) , where a is a constant , i and j are the unit vectors of the x and y axes. Find the flux of the vector E through a sphere of raidus R with its centre at the origin of coordinates.

A particle of mass m moves in pane xy due to the force varying with velocity as F=a(dot(y)-dot(x)j) , where a is a positve constant, i and j are the unit vectors of the x and y axes. At the initial moment t=0 the particle was located at the point x=y=0 and possessed a velocity v_(0) directed along the unit vector j . Find the law of motino x(t), y(t) of the particle, and also the equation of its trajectory.

Let f(x) =ax^(2) -b|x| , where a and b are constants. Then at x = 0, f (x) is

Find the potential varphi (x,y) of an electrostatic field E = 2axyi + a (x^(4) - y^(2)) j , where a is a constant, I and J are the unit vectors of the x and y axes.

The intensity of an electric field depends only on the coordinates x and y as follows, E = (a(xhati +y hatj))/(x^(2)+y^(2)) where, a is constant and hati and hatj are the unit vectors of the x and y axes. Find the charges within a sphere of radius R with the centre at the origin.