Question

3. [Total: 8 pts) The purpose of this problem is to remind you of basic vector manipulation, and to get you familiar with the notation used in this class. Suppose a point charge q > 0 is at rest and located at position r = (2,3), in a two- dimensional Cartesian coordinate system (x,y). Suppose we want information about the electric field E at position r= (6,4). a) 2 pts) We will define the 'script-r' vector 1 =r-r'. Make a sketch of the three vectors , r and r' in the (2,y) plane. b) 2 pts) Find the unit vector 1 = */n, where 1 = . c) 2 pts) Make a new sketch that includes only the two vectors and d) 2 pts Coulomb's law allows us to compute the electric field; in terms of our new vector we can write E(A) = (kq/12). Make a sketch of the vector field E().

Answer 1

r- ar-2 21 + 3 - 4iti À rer + THE X & ñ hits 42+1=517 1 r 41+ M V17 (0.97 0.24) M

u and i can not be drawn in a Single graph in because they have the same direction. so r oreld overlaps with 7. E ) = (ka/22) ку 112 To-r'l' kw 1 (6-2)i + (4-3): KW 25 42 +12 ka 26 Kq Ку (4 ) 17/17 - ako (41+5)

and in our and so is constant field I Here The field F(x,y) = (4,1) 1 are parallel in (hit? ) all the arrows direction