Question

A and B are two concentric circular conductors of centre O and carrying current $I_{1}and{I}_2$ as shown in the figure.$B_{1}and{B}_2$ are magnitudes of magnetic field due to A and B respectively. The net magnetic field at point O is

• A.
  $B_1+B_2$
• B.
  $B_1-B_2$
• C.
  $B_2\times B_1$
• D.
  $\frac{B_2}{B_1}$

Answer 1

The correct option is A

$B_1+B_2$
Magnetic field (B) at the centre of a current (i) carrying conducting loop of radius r,$B=\frac{{\mu }_{0}i}{2r}$



The current in both the loops is in anti-clockwise direction. Hence, the magnetic field at centre O due to them will be perpendicularly outwards $(⨀)$.

Magnetic field at centre O due to loop A, $B_1=\frac{{\mu }_0{I}_0}{2r_1}⨀$

Magnetic field at centre O due to loop B, Magnitude of net magnetic field at the centre O, $B=B_1+B_2=\frac{{\mu }_0}{2}[\frac{I_1}{r_1}+\frac{I_2}{r_2}]⨀$

Hence, the correct answer is option (1).