A six-sided die has a positive charge in the center of each face, and a negative
ID: 1705372 • Letter: A
Question
A six-sided die has a positive charge in the center of each face, and a negative charge embedded in the center. The charge on each face is proportional to the value on the face. The top side of the die is 6; the bottom is 1; the east is 4; the west is 3; the north face is 5; the south is 2. Find the direction of the electric force on the charge in the center. Express your answer as a vector of length one by stating its components in the up, east, and north directions.The unit vector has components __________ in the up, _________ in the east, and ________ in the north directions.
Explanation / Answer
no need for the dimension. Because the distance from the center of the six faces to the center of the cube is the same. so The electric force is proportional to the charges on the six faces. the electric forces are all attractive. let F_bottom = F. then F_top = 6F. F_east = 4F. F_west = 3F. F_north = 5F. F_south = 2F -- so let calc in each direction (bot-top, west-east, north-south). bot-top, 6F-F=5F . in the direction of top force, so its up. west-east. 4F-3F=F. in the direction of east. north-south. 5F-2F=3F. in the direction of north. so in up,east,north. direction of the net vector. 5,1,3 its directional vector is. sqrt(5^2+1^2+3^2)=sqrt(35). so its 5/sqrt(35),1/sqrt(35),3/sqrt(35)