SOLUTION: Hi! I'm struggling with this homework question... I feel like there's not enough information. Could someone help me out? "A point charge +q is held fixed at the origin, and a se

Algebra ->  Vectors -> SOLUTION: Hi! I'm struggling with this homework question... I feel like there's not enough information. Could someone help me out? "A point charge +q is held fixed at the origin, and a se      Log On


   

Question 1165901: Hi! I'm struggling with this homework question... I feel like there's not enough information. Could someone help me out?
"A point charge +q is held fixed at the origin, and a second charge +9q is held fixed at x = 1.0 m. Where should a third charge q be placed so that the net force on it is zero?"
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


The given charge q is at (0,0); the charge 9q is at (1,0).

Let the added charge q be at (b,0).

The distance from (0,0) to (b,0) is b; the distance from (1,0) to (b,0) is 1-b.

The force between any two charges is directly proportional to the sizes of both charges and inversely proportional to the square of the distance between them.

%28q%29%28q%29%2F%28b%5E2%29+=+%28q%29%289q%29%2F%281-b%29%5E2
q%5E2%2Fb%5E2+=+9q%5E2%2F%281-b%29%5E2
9q%5E2%2Fq%5E2+=+%281-b%29%5E2%2Fb%5E2
9+=+%281-b%29%5E2%2Fb%5E2
3+=+%281-b%29%2Fb
3b+=+1-b
4b+=+1
b+=+1%2F4

ANSWER: The additional charge q should be placed at (1/4,0) to make the net force on it zero.