A small current element of length 'd l' and carrying current is placed at (1,1,0) and is carrying current in '+z' direction. If magnetic field at origin be `vecB_(1)` and at point (2,2,0) be `vecB_(2)` then :

Options

A. `|vecB_(1)|=|vecB_(2)|`
B. `vecB_(1)=+vecB_(2)`
C. `|vecB_(1)|=|2vecB_(2)|`
D. `vecB_(1)=-2vecB_(2)`

Answer

A

Explanation

`vecB=(mu_(0))/(4pi)(idveclxxvecr)/(r^(3))` for `B_(1)vecr=(-hati-hatj)`
`thereforevecB_(1)=(mu_(0))/(4pi)(i)/(2sqrt(2)) hatkxx(-hati-hatj)` .....(1)
for `B_(2) vecr=hati+hatj`
`vecB_(2)=(mu_(0))/(4pi)(ihatkxx(hati+hatj))/(2sqrt(2))` .......(2)
from (1) `&` (2)
`vecB_(t)=-vecB_(2)& |vecB_(1)|=|vecB_(2)|`