Question

Two small magnets are placed horizontally,perpendicular to the magnetic meridian.Their north poles are at 30cm East and 20cm west from a compass needle.if the compass needle remains undeflected compare the magnetic moments of the magnets

Answer 1

Dear Student ,
here in this question the needle remains undeflected that means that point the magnetic field is zero .
Now when , the north poles are 30 cm east and 20 cm west from a compass needle then ,
$$\begin{gathered} B_1=\frac{{\mu }_0}{4\pi }\frac{m_1}{{\left(30\right)}^3}and{B}_2=\frac{{\mu }_0}{4\pi }\frac{m_2}{{\left(20\right)}^3} \\ Nowasthe{B}_1=B_2=0then, \\ \frac{{\mu }_0}{4\pi }\frac{m_1}{{\left(30\right)}^3}=\frac{{\mu }_0}{4\pi }\frac{m_2}{{\left(20\right)}^3} \\ \Rightarrow \frac{m_1}{m_2}=\frac{{\left(3\right)}^3}{{\left(2\right)}^3}=\frac{27}{8} \\ \Rightarrow m_1:m_2=27:8 \end{gathered}$$
Regards