Question

A small current element of length $dl$ and carrying current is placed at $(1,1,0)$ and is carrying current in '$+z$' direction. If magnetic field at origin be ${\overrightarrow{B}}_1$ and at point $(2,2,0)$ be ${\overrightarrow{B}}_2$ then

• A. $\overrightarrow{B}=\overrightarrow{B}$
• B. $|{\overrightarrow{B}}_1|=|2{\overrightarrow{B}}_2|$
• C. ${\overrightarrow{B}}_1=-{\overrightarrow{B}}_2$
• D. ${\overrightarrow{B}}_1=-2{\overrightarrow{B}}_2$

Answer 1

The correct option is C ${\overrightarrow{B}}_1=-{\overrightarrow{B}}_2$

Now it is given that a small current carrying element is placed at $(1,1,0)$ and carrying current in $+z$ direction.
Then by using right hand thumb rule we can find the magnetic field lines which would be circular in this case having center at $(1,1,0)$
Now since origin and $(2,2,0)$ are two points which will lie on a circular centered at $(1,1,0)$ therefore, magnitude of magnetic field will be same at both the points.
And we find that origin and $(2,2,0)$ are diametrical opposite points therefore, direction of magnetic field at origin will be just opposite of the direction of magnetic field at $(2,2,0)$