Question

Two infinitely long straight wires lie in the $xy$-plane along the lines $x=\pm R$. The wire located at $x=+R$ carries a constant current $I_1$ and the wire located at $x=-R$ carries a constant current $I_2$. A circular loop of radius $R$ is suspended with its centre at $(0,0,\sqrt{3}R)$ and in a plane parallel to the $xy$-plane. This loop carries a constant current $I$ in the clockwise direction as seen from above the loop. The current in the wire is taken to be positive if it is in the $+\hat{j}$ direction. Which of the following statements regarding the magnetic field $\overrightarrow{B}$ is (are) true ?

• A. If $I_1=I_2$, then $\overrightarrow{B}$ cannot be equal to zero at the origin $(0,0,0)$
• B. If $I_1>0$ and $I_2<0$, then $\overrightarrow{B}$ can be equal to zero at the origin $(0,0,0)$
• C. If $I_1<0$ and $I_2>0$, then $\overrightarrow{B}$ can be equal to zero at the origin $(0,0,0)$
• D. If $I_1=I_2$, then the $z$-component of the magnetic field at the centre of the loop is $(-\frac{{\mu }_{0}I}{2R})$

Answer 1

Answer: (A), (B), (D)

If $I_1=I_2$, then the $z$-component of the magnetic field at the centre of the loop is $(-\frac{{\mu }_{0}I}{2R})$


For option A:
if $I_1=I_2$ then the magnetic field due to infinite wire will be equal to zero. Hence no non-magnetic field will produce on behalf of current carring loop.
Hence, option A is correct.

For option B:
If $i_1>0$ and $i_2<0$ then the magnetic field due to straght line will be in z direction and due to loop it will be at -z direction.
Hence, option B is correct.

For option C:
If $i_1<0$ and $i_2>0$ then the magnetic field due to straght line will be in -z direction and due to loop it will also be in -z direction as well, which cancles each other, hence $B$ can not be zero at origin.
So, option C is wrong.

For option D:
z-component is only because of ring which is $\overrightarrow{B}=\frac{{\mu }_{0}I}{2R}(-\hat{K})$
and hence, option D is correct.