Question

Two circular coils having number of turns 3N and N respectively and carrying equal currents in same sense are placed coaxially, such that they subtend the same solid angle at O. Let $B_0$ be the magnetic field at O due to smaller coil, then

• A. magnetic field at O due to larger coil is $3\sqrt{3}{B}_0$
• B. magnetic field at O due to larger coil is $3B_0$
• C. Net magnetic field at O is $2B_0$
• D. Net magnetic field at O is zero

Answer 1

The correct option is C Net magnetic field at O is $2B_0$

Due to smaller coil $B_0=\frac{{\mu }_0}{4\pi }\frac{2I\left(\pi R^2\right)N}{(R^2+x^2{)}^{\frac{3}{2}}}$
Due to larger coil $B^{\prime }=\frac{{\mu }_0}{4\pi }\frac{2I\left(9\pi R^2\right)3N}{\left[\right(3R{)}^2+(3x{)}^2{]}^{\frac{3}{2}}}=\frac{27}{27}{B}_0=B_0$