A point charge `mu` is placed at origin. Let `vecE_(A), vec E_(B), and vecE_(C)` be the electirc field at three points A (1,2,3), B (1,1,-1), and C(2,2,2) due to charge `mu`. Then

Options

A. `vecE_(A)_|_vecE_(B)`
B. `vecE_(A)||vecE_(B)`
C. `|vecE_(B)| = 4|vecE_(C)|`
D. `vecE_(B) = 16 | vecE_(C)|`

Answer

A, C

Explanation

a.,c.
`vecE_(A)` is along `OA` and `OA=hati+2hatj+3hatK`
`vecE_(B)` is along `OB=hati+hatj-hatK`
Since `oAxxOB=(hati+2hatj+3hatK)xx(hati+hatj-hatk)=0`
So `OAbotOBrArrvecE_(A)botvecE_(0)`
So, option (a) is correct.
Since `E_(B)=(kq)/([OB]^(2))=(kq)/(3)`
`E_(C)=(kq)/([OC]^(2))=(kq)/(12)`
So `(E_(B))/(E_(C))=4` or `|vecE_(B)|=4|vecE_(C)|`
So, option (c) is correct.
Option (b) and (d) are wrong from the explanation.