Discussion Forum

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B_1.  When the dipole moment is doubled by keeping the current costant, the magnetic field at the centre of the loop is B₂. The ratio B₁/B₂

Answer:

Explanation:

Key Idea As m=IA, so to change dipole moment (current is kept constant), we have to change radius of loop

initially,$m=I\pi R^{2} $ and $B_{1}=\frac{\mu_{0}I}{2R_{1}}$

Finally,$m^{'}=2m = I\pi R_2^2$

$2I\pi R_2^2=I\pi R_2^2$

or,  $R_{2}=\sqrt{2}R_{1}$

So, $B_{2}=\frac{\mu_{0}I}{2(R_{2})}=\frac{\mu_{0}I}{2\sqrt{2}(R_{1})}$

Hence, $ratio\frac{B_{1}}{B_{2}}= \frac{\frac{\mu_{0}I}{2R_{2}}}{\frac{\mu_{0}I}{2\sqrt{2}R_{1}}}$

$\frac{B_{1}}{B_{2}}=\sqrt{2}$